Derivative Topics

Master core derivative rules with clear explanations, formulas and real applications.

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Chain Rule

IntermediateDifficulty

Complete guide to differentiating composite functions using the chain rule.

Examples

(x^2 + 1)^3sin(2x^2)e^(3x^2 + 2x)
3 个示例
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×

Product Rule

BasicDifficulty

Derivative of the product of two functions with formula and examples.

Examples

x^2 · sin(x)e^x · cos(x)(x^2 + 1) · (x - 2)
3 个示例
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÷

Quotient Rule

IntermediateDifficulty

Derivative of the quotient of two functions with proofs and tips.

Examples

(x^2 + 1) / (x - 1)sin(x) / xe^x / (x + 1)
3 个示例
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xⁿ

Power Rule

BasicDifficulty

Fundamental rule for differentiating power functions.

Examples

x^3x^(1/2)x^(-2)+1 more
4 个示例
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△

Trigonometric Derivatives

IntermediateDifficulty

Derivatives of sine, cosine, tangent and more.

Examples

sin(x)cos(x)tan(x)+1 more
4 个示例
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eˣ

Exponential Derivatives

BasicDifficulty

Derivatives of e^x and a^x with applications.

Examples

e^x2^xe^(3x)+1 more
4 个示例
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ln

Logarithmic Derivatives

IntermediateDifficulty

Derivatives of ln(x) and log_a(x) with techniques.

Examples

ln(x)log₂(x)log₁₀(x)+1 more
4 个示例
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∂y/∂x

Implicit Differentiation

AdvancedDifficulty

Differentiate implicit functions with step-by-step method.

Examples

x^2 + y^2 = 1x^3 + xy + y^3 = 1e^(x + y) = x^2 + y^2
3 个示例
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⟨

Parametric Derivatives

AdvancedDifficulty

Derivatives for parametric equations with geometric insights.

Examples

x = cos(t), y = sin(t)x = e^t, y = t^2x = 2t, y = t^2
3 个示例
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Why choose DerivCalc Pro?

🎯

Smart algorithms

AI-powered engine that accurately handles complex expressions

📚

Detailed steps

Every calculation comes with a complete derivation and explanation

📊

Visual charts

Interactive graphs to understand the geometric meaning of derivatives

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Multiple formats

Supports LaTeX output for academic and reporting use

Recommended Learning Path

🌱 Beginner Path

  1. 1
    Power Rule
    Master the basic differentiation rule
  2. 2
    Product Rule
    Differentiate the product of two functions
  3. 3
    Quotient Rule
    Understand derivatives of fractional functions

🚀 Intermediate Path

  1. 1
    Chain Rule
    Handle composite functions effectively
  2. 2
    Trigonometric Derivatives
    Master derivatives of periodic functions
  3. 3
    Exponential Derivatives
    Learn derivatives of exponential and logarithmic functions

🔬 Advanced Path

  1. 1
    Implicit Differentiation
    Techniques for complex function relationships
  2. 2
    Parametric Derivatives
    Understand derivatives of parameterized functions
  3. 3
    Higher-order Derivatives
    Explore partial derivatives, gradients and advanced concepts