Calculus AB Derivatives

Limit definition of derivative

f((x+h)-f(x)) / h and or (f(x)-f(a)) / x-a

Tangent line equation

y-y1 = m(x-x1)

instantaneous rate of change

f’(a) = f(x)-f(a)/x-a

Average rate of change over a closed interval

f(b)-f(a)/b-a

Power rule

derivative of x^n = nx^(n-1)

Product rule

(fg)’ = (f’ * g) + (f * g’)

Quotient rule

f’/g’ = (f’*g) - (f*g’) / g²

e^x derivative

e^x

derivative of ln(x)

1/x

derivative of sin(x)

cos(x)

derivative of cos(x)

-sin(x)

derivative of tan(x)

sec²(x)

derivative of sec(x)

sec(x)tan(x)

derivative of csc(x)

-csc(x)cot(x)

derivative of cot(x)

-csc²(x)