Derivatives

y’ (axⁿ)

n * ax^n-1

y’ (e^x)

e^x

y’ (ln(x))

1/x

y’ (sin(x))

cos(x)

y’ cos(x))

-sin(x)

y’ (tan(x))

sec²(x)

y’ (cot(x))

-csc²(x)

y’ (sec(x))

sec(x)tan(x)

y’ (csc(x))

-csc(x)cot(x)

y’ (a^x)

a^x * ln(a)

y’ (log_a(x))

1/x * 1/ln(a)

constant rule

(d/dx)(k)=0

sum rule

d/dx[f(x)+g(x)]=f’(x)+g’(x)

difference rule

d/dx[f(x)-g(x)]=f’(x)-g’(x)

constant multiple rule

d/dx[kf(x)]=kf’(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)