Derivatives in Calculus

In this set of flashcards are all the derivatives and rules you need to know in AP Calculus AB.

\cos(u)\cdot\frac{du}{dx}

\frac{d}{dx}\left(\sin(u)\right)=

-\sin(u)\cdot\frac{du}{dx}

\frac{d}{dx}\left(\cos(u)\right)=

\sec^{2}(u)\cdot\frac{du}{dx}

\frac{d}{dx}\left(\tan(u)\right)=

\sec(u)\tan(u)\cdot\frac{du}{dx}

\frac{d}{dx}\left(\sec(u)\right)=

-\csc^{2}(u)\cdot\frac{du}{dx}

\frac{d}{dx}\left(\cot(u)\right)=

-\csc(u)\cot(u)\cdot\frac{du}{dx}

\frac{d}{dx}\left(\csc(u)\right)=

n\cdot x^{n-1}

\frac{d}{dx}\left(x^{n}\right)=

n\cdot u^{n-1}\cdot\frac{du}{dx}

\frac{d}{dx}\left(u^{n}\right)=

g\left(x\right)f^{\prime}\left(x\right)+f\left(x\right)g^{\prime}\left(x\right)

\frac{d}{dx}\left(f(x)\cdot g(x)\right)=

\frac{g\left(x\right)f^{\prime}\left(x\right)-f\left(x\right)g^{\prime}\left(x\right)}{g(x)^2}

\frac{d}{dx}\left(\frac{f(x)}{g(x)}\right)=

f’(g(x))\cdot g’(x)

\frac{d}{dx}\left(f(g(x))\right)=

\ln(a)\cdot a^x

\frac{d}{dx}\left(a^{x}\right)=

\ln(a)\cdot a^{u}\cdot\frac{du}{dx}

\frac{d}{dx}\left(a^{u}\right)=

e^{u}\cdot\frac{du}{dx}

\frac{d}{dx}\left(e^{u}\right)=

\frac{1}{u}\cdot \frac{du}{dx}

\frac{d}{dx}\left(\ln(u)\right)=

\frac{1}{\ln(b)\cdot u}\cdot \frac{du}{dx}

\frac{d}{dx}\left(\log_{b}(u)\right)=

\frac{1}{f’\left(f^{-1}(x)\right)}

\frac{d}{dx}\left(f^{-1}(x)\right)=

\frac{1}{\sqrt{1-u^{2}}}\cdot\frac{du}{dx}

\frac{d}{dx}\left(\arcsin(u)\right)=

-\frac{1}{\sqrt{1-u^2}}\cdot\frac{du}{dx}

\frac{d}{dx}\left(\arccos(u)\right)=

\frac{1}{1+u^{2}}\cdot\frac{du}{dx}

\frac{d}{dx}\left(\arctan(u)\right)=