derivative rules

Expontial Base e?

d/dx e^x=e^x

Expontial Base b?

d/dx b^x=ln(b)b^x

chain rule & expontial base e

d/dx e^kx=ke^kx

Log Base b

d/dx logb(x)=1/ln(b)x

Log Base e

d/dx ln(x)=d/dx loge(x)=1/x

Chain and log Base e

d/dx ln|x|=1/x

d/dx sin(x)

cos(x)

d/dx cos(x)

-sin(x)

d/dx tan(x)

sec^2(x)

d/dx cot(x)

-csc^2(x)

d/dx sec(x)

sec(x)tan(x)

d/dx csc(x)

-csc(x)cot(x)

Constant rule

d/dx k=0

Powe rule

d/dx x^n=nx^n-1

Sum/difference rule

d/dx f(x)-g(x)=f'(x)-+g'(x)

d/dx f(x)-g(x)=f'(x)+-g'(x)

f'(x)-+g'(x)

f'(x)+-g'(x)

Constant Multiple rule

d/dx Kf(x)=k d/dx f(x)

Product rule

d/dx (f(x)g(x))=f'(x)g(x)+f(x)g'(x)

Quotient rule

Hi de, lo, Hi, lo de, lo lo

Chain rule

f'(g(x))g'(x)

General Power rule

d/dx (y(x))^n=n(y(x))^n-1y'(x)=n(y(x)^n-1 dy/dx