Calculus formula sheet

Hi there. Here’s my condensed formula sheet. It solves 99.9% of your headaches and saves time from memorizing them.

Derivative

$$
\begin{align}
\cfrac{d}{dx}\left(a\right) &= 0\\
\cfrac{d}{dx}\left(ax^n\right) &= nax^{n-1}\\
\cfrac{d}{dx}\left(uv\right) &= v\cfrac{du}{dx}+u\cfrac{dv}{dx}\\
\cfrac{d}{dx}\left(\cfrac{u}{v}\right) &= \cfrac{v\cfrac{du}{dx}-u\cfrac{dv}{dx}}{v^2}\\
\cfrac{d}{dx}\left(e^u\right) &= \cfrac{du}{dx}e^u\\
\cfrac{d}{dx}\left(a^u\right) &= \cfrac{du}{dx}a^u\times\ln\left(a\right)\\
\end{align}
$$

Trigonometry Derivative

$$
\begin{align}
\cfrac{d}{dx}\left(sin(u)\right) &= cos(u)\times\cfrac{du}{dx}\\
\cfrac{d}{dx}\left(cos(u)\right) &= -sin(u)\times\cfrac{du}{dx}\\
\cfrac{d}{dx}\left(tan(u)\right) &= sec^2(u)\times\cfrac{du}{dx}\\
\cfrac{d}{dx}\left(cot(u)\right) &= -csc^2(u)\times\cfrac{du}{dx}\\
\cfrac{d}{dx}\left(sec(u)\right) &= sec(u)tan(u)\times\cfrac{du}{dx}\\
\cfrac{d}{dx}\left(csc(u)\right) &= -csc(u)cot(u)\times\cfrac{du}{dx}\\
\\
\cfrac{d}{dx}\left(sin^n(u)\right) &= n\times sin^{n-1}(u)cos(u)\times\cfrac{du}{dx}\\
\cfrac{d}{dx}\left(cos^n(u)\right) &= -n\times cos^{n-1}(u)sin(u)\times\cfrac{du}{dx}\\
\cfrac{d}{dx}\left(tan^n(u)\right) &= n\times tan^{n-1}(u)sec^2(u)\times\cfrac{du}{dx}\\
\cfrac{d}{dx}\left(cot^n(u)\right) &= -n\times cot^{n-1}(u)csc^2(u)\times\cfrac{du}{dx}\\
\cfrac{d}{dx}\left(sec^n(u)\right) &= n\times sec^{n-1}(u)sec(u)tan(u)\times\cfrac{du}{dx}\\
\cfrac{d}{dx}\left(csc^n(u)\right) &= -n\times csc^{n-1}(u)csc(u)cot(u)\times\cfrac{du}{dx}\\
\end{align}
$$

Integration

$$
\begin{align}
\int{ax^n}{dx} &= \cfrac{ax^{n+1}}{n+1}\\
\int{\cfrac{1}{u}}{dx} &= \cfrac{1}{u}ln(u)+c\\
\int{e^{ax}}{dx} &= \cfrac{1}{a}e^{ax}+c\\
\end{align}
$$

Trigonometry Integration

$$
\begin{align}
\int{sin(ax)}{dx} &= -\cfrac{1}{a}cos(ax)\\
\end{align}
$$