Derivatives: chain rule and other advanced topics videos

Chain rule

Common chain rule misunderstandings

Worked example: Derivative of cos³(x) using the chain rule

Identifying composite functions

Worked example: Derivative of √(3x²-x) using the chain rule

Worked example: Derivative of ln(√x) using the chain rule

Worked example: Chain rule with table

Derivative of aˣ (for any positive base a)

Derivative of logₐx (for any positive base a≠1)

Worked example: Derivative of 7^(x²-x) using the chain rule

Worked example: Derivative of log₄(x²+x) using the chain rule

Worked example: Derivative of sec(3π/2-x) using the chain rule

Worked example: Derivative of ∜(x³+4x²+7) using the chain rule

Implicit differentiation

Showing explicit and implicit differentiation give same result

Worked example: Evaluating derivative with implicit differentiation

Worked example: Implicit differentiation

Implicit differentiation (advanced example)

Implicit differentiation (advanced example)

Implicit differentiation (advanced example)

Derivative of ln(x) from derivative of 𝑒ˣ and implicit differentiation

Derivatives of inverse functions

Derivatives of inverse functions: from table

Derivatives of inverse functions: from equation

Derivative of inverse sine

Derivative of inverse tangent

Derivative of inverse cosine

Manipulating functions before differentiation

Differentiating functions: Find the error

Differentiating using multiple rules: strategy

Applying the chain rule and product rule

Derivative of sin(ln(x²))

Applying the chain rule twice

Derivative of eᶜᵒˢˣ⋅cos(eˣ)

Product rule to find derivative of product of three functions

Second derivatives

Second derivatives (implicit equations): find expression

Second derivatives (implicit equations): evaluate derivative

Disguised derivatives

Composite exponential function differentiation

Worked example: Composite exponential function differentiation

Proof: Differentiability implies continuity

Chain rule proof

Quotient rule from product & chain rules

If function u is continuous at x, then Δu→0 as Δx→0