Derivative Rules

These flashcards cover the key derivative rules and formulas.

Derivative of a constant multiplied by a function

If f(x) = kx, then f'(x) = k.

Product Rule for derivatives

If f(x) = u*v, then f'(x) = u'v + uv'.

Derivative of sine function

If f(x) = sin(x), then f'(x) = cos(x).

Derivative of cosine function

If f(x) = cos(x), then f'(x) = -sin(x).

Derivative of tangent function

If f(x) = tan(x), then f'(x) = sec²(x).

Derivative of secant function

If f(x) = sec(x), then f'(x) = sec(x)tan(x).

Derivative of cosecant function

If f(x) = csc(x), then f'(x) = -csc(x)cot(x).

Power Rule for derivatives

If f(x) = x^n, then f'(x) = nx^(n-1).

Derivative of cotangent

function

Definition: If f(x) = cot(x), then f'(x) = -csc^2(x).

Quotient rule

U’V-UV’ / V²