The Derivative and Differentiation Rules

Define the derivative as the limit of a difference quotient.

Interpret the derivative as the gradient (slope) of a tangent line and as an instantaneous rate of change.

Compute derivatives of polynomial and power functions using the power rule.

Compute derivatives of composite functions using the chain rule.

Find derivatives of trigonometric functions.

Find derivatives of exponential and logarithmic functions.

Use implicit differentiation to find derivatives of implicitly defined functions.