

Basic
Differentiation Formulas

DERIVATIVE OF A CONSTANT FUNCTION: EXAMPLES: THE POWER RULE: If is a positive integer, then EXAMPLES: Differentiate (a) (b) (c) THE POWER RULE (GENERAL VERSION): If is any real number, then EXAMPLES: Differentiate (a) (b) (c) (d) (e) (f) (g) THE CONSTANT MULTIPLE RULE: If is a constant and is a differentiable function, then EXAMPLE: Differentiate . EXAMPLE: Find equations of the tangent line and normal line to the curve at the point . THE SUM/DIFFERENCE RULE: If and are both differentiable functions, then or EXAMPLE: Differentiate . EXAMPLE: Differentiate . REMARK: We can combine two previous rules in one. If are constants and are both differentiable functions, then or EXAMPLE: Differentiate . THE DERIVATIVE OF THE SINE AND COSINE FUNCTIONS: We have and EXAMPLE: Differentiate . EXAMPLE: Find if . 