Standard Derivatives

Level 1 - Math I (Physics) topic page in Differentiation.

Memorize these basic derivatives:

Power

\[\frac{d}{dx}[x^n] = nx^{n-1}\]

Exponential

\[\frac{d}{dx}[e^x] = e^x\]

Log

\[\frac{d}{dx}[\ln(x)] = \frac{1}{x}\]

Sine

\[\frac{d}{dx}[\sin(x)] = \cos(x)\]

Cosine

\[\frac{d}{dx}[\cos(x)] = -\sin(x)\]

Tangent

\[\frac{d}{dx}[\tan(x)] = \sec^2(x)\]

Arcsin

\[\frac{d}{dx}[\arcsin(x)] = \frac{1}{\sqrt{1-x^2}}\]

Arctan

\[\frac{d}{dx}[\arctan(x)] = \frac{1}{1+x^2}\]