Calculus - Derivatives

derivative of x^p

px^p-1

derivative of sqrt(x)

1/2*sqrt(x)

derivative of a^x

ln a * a^x

derivative of e^x

e^x

derivative of log_ax

1/(ln a * x)

derivative of ln x

1/x

derivative of sin(x)

cos(x)

derivative of cos(x)

-sin(x)

derivative of tan(x)

sec²x

derivative of cot(x)

-csc²x

derivative of sec(x)

sec(x)tan(x)

derivative of csc(x)

-csc(x)cot(x)

derivative of arcsin(x)

1/sqrt(1-x²)

derivative of arccos(x)

-1/sqrt(1-x²)

derivative of arctan(x)

1/(1+x²)

derivative of arccot(x)

-1/(1+x²)

derivative of arcsec(x)

1/(|x|*sqrt(x²-1))

derivative of arccsc(x)

-1/(|x|*sqrt(x²-1))

derivative of e^kx

ke^kx

derivative of a^kx

ln a * k * a^kx

Product Rule

(F S)^’ = F * S^‘ + F^’ * S

Quotient Rule

(T/B)^’ = (B * T^’-T * B^’)/B²

Chain Rule

d/dx f(g(x)) = f^’(g(x)) * g^’(x)