Khan Academy

Limit expression for the derivative of function (graphical)-video (K-A)

The derivative of x² at any point using the formal definition (K-A)

The derivative of x² at x=3 using the formal definition (K-A)

Worked example: Derivative as a limit (K-A)

Worked example: Derivative from limit expression (K-A)

Basic derivative rules (K-A)

Basic derivative rules: find the error (K-A)

Basic derivative rules: table (K-A)

Justifying the basic derivative rules (K-A)

Derivative of ln(x) (K-A)

Derivative of 𝑒ˣ (K-A)

Derivatives of sin(x) and cos(x) (K-A)

Proof: the derivative of ln(x) is 1/x (K-A)

Proof: The derivative of 𝑒ˣ is 𝑒ˣ (K-A)

Proving the derivatives of sin(x) and cos(x) (K-A)

Worked example: Derivatives of sin(x) and cos(x) (K-A)

Derivatives of sec(x) and csc(x) (K-A)

Derivatives of tan(x) and cot(x) (K-A)

Differentiability and continuity (K-A)

Differentiability at a point: algebraic (function is differentiable) (K-A)

Differentiability at a point: algebraic (function isn't differentiable) (K-A)

Differentiability at a point: graphical (K-A)

Proof: Differentiability implies continuity (K-A)

Estimating derivatives-video (K-A)

Justifying the power rule (K-A)