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Differentiation

Proofs

 Tutorial Name Tutorial Description Limit Definition of Derivative Shows the derivation of the limit definition of a derivative. Constant Rule Proves the constant rule of differentiation. Power Rule Proves the power rule of differentiation. Constant Multiple Rule Proves the constant multiple rule of differentiation. Sum and Difference Rules Proves the sum and difference rules of differentiation. Product Rule Proves the product rule for differentiation. Quotient Rule Proves the quotient rule for differentiation. Chain Rule Proves the chain rule for differentiation. Derivative of Sine Proves the derivative rule for sine. Derivative of Cosine Proves the derivative rule for cosine. Derivative of Tangent Proves the derivative rule for tangent. Derivative of Secant Proves the derivative rule for secant. Derivative of Cosecant Proves the derivative rule for cosecant. Derivative of Cotangent Proves the derivative rule for cotangent. Derivative of Absolute Value of x Walks through the derivation of the derivative of the absolute value of x.  This gives insight into why functions are non-differentiable spanning intervals with sharp turns.

Tutorials

 Tutorial Name Tutorial Description An Introduction to The Derivative (Part 1) The Tangent Line Problem, Limit Definition of a Derivative. An Introduction to The Derivative (Part 2) Derivatives using limit definition of derivative. An Introduction to The Derivative (Part 3) Alternate Form of the Derivative, Diffentiability. An Introduction to The Derivative (Part 4) Differentiability, Constant Rule, Power Rule, An Introduction to The Derivative (Part 5) Constant Multiple Rule, Sum and Difference Rules, The Product Rule. An Introduction to The Derivative (Part 6) The Quotient Rule,  The Chain Rule. An Introduction to The Derivative (Part 7) Derivatives of Trigonometric Functions (overview) An Introduction to The Derivative (Part 8) Implicit Differentiation. An Introduction to The Derivative (Part 9) Implicit Differentiation (continued), additional differentiation problems. Limit Definition of Derivative