Unit 3: Derivative Rules

Constant Rule

d/dx (c) = 0

Constant Multiple Rule

d/dx [c f(x)] = c f’(x)

Power Rule

d/dx (x^n) = nx^n-1

Sum Rule

d/dx [f(x) + g(x)] = f’(x) + g’(x)

Difference Rule

d/dx [f(x) - g(x)] = f’(x) - g’(x)

Product Rule

d/dx [f(x)g(x)] = f’(x)g(x) + f(x)g’(x)

Quotient Rule

d/dx [f(x)/g(x)] = f(x)g’(x) - f(x)g’(x) / [g(x)]^2

Chain Rule

d/dx f(g(x)) = f’(g(x))*g’(x)

Exponential

d/dx [a^x] = (a^x)*ln(a)

Exponential, natural base

d/dx [e^x] = e^x

Logarithmic

d/dx [loga(x)] = 1/xln(a)

Natural Logarithms

d/dx [ln(x)] = 1/x

d/dx (e^g(x))

e^g(x)*g’(x)

d/dx (a^g(x))

ln(a)*a^g(x)*g’(x)

d/dx ln(g(x))

g’(x)/g(x)

d/dx (loga(g(x)))

g’(x)/g(x)*ln(a)

d/dx sin(x)

cos(x)

d/dx cos(x)

-sin(x)

d/dx tan(x)

sec²(x)

d/dx csc(x)

-csc(x)cot(x)

d/dx sec(x)

sec(x)tan(x)

d/dx cot(x)

-csc²(x)