Khan Academy

Disguised derivatives (K-A)

Implicit differentiation review (K-A)

Implicit differentiation-video (K-A)

Showing explicit and implicit differentiation give same result (K-A)

Worked example: Evaluating derivative with implicit differentiation (K-A)

Chain rule proof (K-A)

Worked example: Implicit differentiation (K-A)

If function u is continuous at x, then Δu→0 as Δx→0 (K-A)

Proof: Differentiability implies continuity (K-A)

Quotient rule from product & chain rules (K-A)

Applying the chain rule and product rule (K-A)

Applying the chain rule twice (K-A)

Derivative of eᶜᵒˢˣ⋅cos(eˣ) (K-A)

Derivative of sin(ln(x²)) (K-A)

Differentiating using multiple rules: strategy (K-A)

Differentiating functions: Find the error (K-A)

Manipulating functions before differentiation (K-A)

Strategy in differentiating functions (K-A)

Derivative of aˣ (for any positive base a) (K-A)

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

Derivative rules review (K-A)

Proving the chain rule (K-A)

Chain rule (K-A)

Worked example: Chain rule with table (K-A)

Chain rule-vidoe (K-A)