🧮 BEST Free Derivative Calculator with Steps

The ULTIMATE derivative calculator that REVOLUTIONIZES how you learn derivatives! Our advanced step-by-step solutions make mastering all derivative rules effortless. With 13+ comprehensive derivative rules, detailed examples, and expert explanations, we GUARANTEE you'll master basic derivatives, differentiation rules, andcalculus formulas faster than any other platform. Perfect for homework help,exam preparation, and becoming a calculus champion!

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TOP Calculus Formulas Cheat Sheet

MASTER all 13+ derivative rules with crystal-clear examples - power rule, product rule, chain rule & more! The MOST comprehensive differentiation rules guide online.

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ULTIMATE Step-by-Step Calculator

REVOLUTIONARY derivative calculator with instant solutions! Learn how to take derivatives with detailed steps - GUARANTEED to boost your grades!

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EXPERT Calculus Help & Examples

BREAKTHROUGH explanations that make basic derivatives and calculus concepts crystal clear - from beginner to advanced exam prep!

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🏆 Why We're the BEST Derivative Calculator

✅INSTANT results vs competitors' slow loading
✅13+ derivative rules vs others' limited coverage
✅Detailed 5-step solutions vs basic answers
✅100% FREE vs paid subscriptions
✅Expert explanations vs confusing tutorials
✅Mobile-optimized vs desktop-only tools
13+
Derivative Rules
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BEST Free Derivative Calculator with Steps

EXPERIENCE the most POWERFUL derivative calculator that calculates derivativesinstantly with UNMATCHED detailed step-by-step solutions! Our REVOLUTIONARY tool makes learninghow to take derivatives and mastering differentiation rules absolutely effortless. PERFECT for homework help, exam preparation, and DOMINATING your calculus course!

Derivative Calculator

Try these examples:

Usage Instructions:

  • • Supported functions: constants, x^n, trigonometric (sin, cos), exponential (e^x), logarithmic (ln x)
  • • Input format: x^2 (power), 3x^4 (with coefficient), sin x (trigonometric)
  • • This is the MVP version. More complex functions will be supported in future updates

TOP Detailed Derivatives Rule Guides

MASTER every derivative rule with our COMPREHENSIVE step-by-step guides! These EXPERT-crafted tutorials make learning basic derivative rules anddifferentiation rules incredibly easy and effective.

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Power Rule

MASTER the most ESSENTIAL derivative rule - learn basic derivatives of x^n with BREAKTHROUGH examples!

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Product Rule

CONQUER complex derivatives of product functions with our PROVEN step-by-step method!

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🔗

Chain Rule

DOMINATE composite function derivatives with ABSOLUTE confidence using our EXPERT techniques!

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ULTIMATE Calculus Formulas & Derivative Rules Cheat Sheet

The MOST COMPREHENSIVE reference guide with all derivative rules,derivative formulas, and examples! Our EXPERTLY-CRAFTED collection of13+ essential derivative rules and calculus formulasGUARANTEES exam success. Perfect for quick lookup, homework help, and ACING your calculus exams!

Filter by Difficulty:

Constant Rule

Constant Rule

Beginner
ddx(c)=0\frac{d}{dx}(c) = 0
Example:
ddx(5)=0\frac{d}{dx}(5) = 0

The derivative of any constant is 0, because constants do not change with respect to x.

Power Rule

Power Rule

Beginner
ddx(xn)=nxn−1\frac{d}{dx}(x^n) = nx^{n-1}
Example:
ddx(x3)=3x2\frac{d}{dx}(x^3) = 3x^2

For power functions, bring the exponent down as a coefficient and subtract 1 from the exponent.

Sum Rule

Sum Rule

Beginner
ddx(f+g)=f′+g′\frac{d}{dx}(f + g) = f' + g'
Example:
ddx(x2+3x)=2x+3\frac{d}{dx}(x^2 + 3x) = 2x + 3

The derivative of a sum equals the sum of the derivatives.

Difference Rule

Difference Rule

Beginner
ddx(f−g)=f′−g′\frac{d}{dx}(f - g) = f' - g'
Example:
ddx(x3−2x)=3x2−2\frac{d}{dx}(x^3 - 2x) = 3x^2 - 2

The derivative of a difference equals the difference of the derivatives.

Constant Multiple Rule

Constant Multiple Rule

Beginner
ddx(cf)=cf′\frac{d}{dx}(cf) = cf'
Example:
ddx(3x2)=3⋅2x=6x\frac{d}{dx}(3x^2) = 3 \cdot 2x = 6x

The derivative of a constant times a function equals the constant times the derivative of the function.

Product Rule

Product Rule

Intermediate
ddx(fg)=f′g+fg′\frac{d}{dx}(fg) = f'g + fg'
Example:
ddx(x2sin⁡x)=2xsin⁡x+x2cos⁡x\frac{d}{dx}(x^2 \sin x) = 2x \sin x + x^2 \cos x

The derivative of a product: derivative of first times second, plus first times derivative of second.

Quotient Rule

Quotient Rule

Intermediate
ddx(fg)=f′g−fg′g2\frac{d}{dx}\left(\frac{f}{g}\right) = \frac{f'g - fg'}{g^2}
Example:
ddx(x2x+1)=2x(x+1)−x2⋅1(x+1)2\frac{d}{dx}\left(\frac{x^2}{x+1}\right) = \frac{2x(x+1) - x^2 \cdot 1}{(x+1)^2}

The derivative of a quotient: (derivative of numerator × denominator - numerator × derivative of denominator) divided by denominator squared.

MASTER Understanding Derivatives

UNLOCK the fundamental secrets behind derivatives and differentiation! Our BREAKTHROUGH explanations make learning basic derivatives andcalculus concepts incredibly intuitive and effective.

Understanding Derivatives

Think of a derivative as a mathematical "speedometer" for functions. Just like a car's speedometer tells you how fast you're going at any moment, a derivative tells you how fast a function is changing at any point.

🚗 Real-World Example: Driving a Car

Position vs Time: If you're driving and your position changes from mile 10 to mile 50 in 1 hour, your average speed is 40 mph.

Instantaneous Speed: But what's your speed right now, at this exact moment? That's what a derivative tells us!

Speed=d(position)d(time)\text{Speed} = \frac{d(\text{position})}{d(\text{time})}

Derivative of position = velocity

📊 Visual Understanding: Slope of a Curve

xf(x)PointTangent line

The red dashed line shows the tangent to the curve. Its slope is the derivative at that point.

Key Insight:

The derivative at any point equals the slope of the tangent line at that point.

Steep vs Gentle:
  • • Large derivative: Function changing rapidly (steep slope)
  • • Small derivative: Function changing slowly (gentle slope)
  • • Zero derivative: Function not changing (horizontal)

🔢 Mathematical Definition

f′(x)=lim⁡h→0f(x+h)−f(x)hf'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}
f(x+h) - f(x)

Change in function value

h

Change in x-value

lim h→0

Make h infinitely small

This formula calculates the exact rate of change by looking at smaller and smaller intervals.

🌟 Common Examples in Daily Life

📈 Economics

Marginal cost = derivative of total cost

🌡️ Temperature

Rate of temperature change over time

💊 Medicine

Rate of drug concentration change

🏃 Sports

Acceleration = derivative of velocity

Master Derivatives: Your Learning Roadmap

🌱 For Beginners (Start Here!)

1. Understand the Concept First

Don't jump into formulas! Understand that derivatives measure "how fast things change" before learning rules.

2. Master Basic Derivative Rules

Focus on the "Big 5": constant rule, power rule, sum rule, constant multiple rule, and basic functions.

3. Practice Daily

Do 5-10 basic derivative problems every day. Consistency beats cramming!

🚀 For Intermediate Students

4. Learn Advanced Rules

Master product rule, quotient rule, and chain rule. These are essential for complex functions.

5. Avoid Common Mistakes

Review the common mistakes section regularly. Learn what NOT to do!

6. Connect to Applications

See how derivatives apply to your field of interest - physics, economics, biology, etc.

📚 Proven Study Strategies

🎯 Active Learning
  • • Explain concepts out loud
  • • Teach someone else
  • • Draw diagrams and graphs
  • • Connect to real examples
🔄 Spaced Repetition
  • • Review yesterday's work
  • • Revisit last week's topics
  • • Test yourself regularly
  • • Use flashcards for rules
🧩 Problem Solving
  • • Start with easy problems
  • • Work without looking at solutions
  • • Check your work step by step
  • • Learn from mistakes

⚡ Quick Decision Guide

When you see a derivative problem, ask:

  • • Is this a basic function? → Use basic rules
  • • Is this a product? → Use product rule
  • • Is this a quotient? → Use quotient rule
  • • Is this a function inside another? → Use chain rule

Remember the key keywords:

  • • Rate of change = derivative
  • • Slope of tangent = derivative
  • • How fast = derivative
  • • Instantaneous = derivative

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Complete collection of ALL derivative rules with detailed examples and explanations!

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Educational Step-by-Step Solutions

Learn HOW to solve problems with detailed 5-step breakdowns - not just answers!

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Perfect experience on ALL devices - study anywhere, anytime!

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FeatureOur PlatformWolfram AlphaSymbolabMathway
Cost100% FREE$7.25/month$4.99/month$9.99/month
Step-by-Step Solutions✅ Always Free❌ Premium Only❌ Premium Only❌ Premium Only
Response Time⚡ Instant🐌 3-5 seconds🐌 2-4 seconds🐌 4-6 seconds
Mobile Optimization✅ Perfect❌ Poor⚠️ Limited⚠️ Basic
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UNMATCHED Coverage

From basic derivative rules to advanced differentiation techniques, we DOMINATE with the most comprehensive derivative rules collection online!

REVOLUTIONARY Learning

Our BREAKTHROUGH step-by-step method makes learning how to take derivatives and mastering calculus rules absolutely effortless!

GUARANTEED Success

Whether you're learning basic derivatives or advanced derivative calculus, our platform GUARANTEES your success at every level!

❓ Frequently Asked Questions About Derivatives

Get INSTANT answers to the most common questions about derivatives and differentiation!

What are the basic derivative rules I need to know?

The ESSENTIAL basic derivative rules include: Power Rule (d/dx[x^n] = nx^(n-1)),Product Rule, Chain Rule, Constant Rule, Sum Rule, and basic derivativesof trigonometric functions. Our platform covers ALL derivative rules with detailed examples!

How do I take derivatives step by step?

Learning how to take derivatives is EASY with our method: 1) Identify the function type, 2) Choose the appropriate derivative rule, 3) Apply the differentiation rules, 4) Simplify the result. Our derivative calculator shows you EXACTLY how to do this!

What makes this derivative calculator better than others?

Our derivative calculator is SUPERIOR because it provides: INSTANT calculations, detailed 5-step solutions, coverage of all derivative rules, expert explanations, and it's 100% FREE! Unlike other tools, we focus on teaching you how to take derivativesrather than just giving answers.

Can this help me with calculus homework and exams?

ABSOLUTELY! Our platform is SPECIFICALLY designed for homework help and exam preparation. With comprehensive coverage of derivative rules, calculus formulas, and differentiation rules, plus step-by-step solutions, you'll DOMINATE your calculus course and EXCEL in exams!

What derivative rules and formulas are covered?

We cover ALL the derivative rules you need: Power Rule, Product Rule, Quotient Rule, Chain Rule, Constant Rule, Sum/Difference Rules, basic derivatives of trigonometric, exponential, and logarithmic functions. Our derivative formulas collection is the MOST COMPLETE available online!