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Basic Derivatives

· Sum Rule for Differentiation
$\frac{d}{dx}\left[f\left(x\right)+g\left(x\right)\right]=\frac{d}{dx}f\left(x\right) + \frac{d}{dx}g\left(x\right)$
· Derivative of a Constant
$\frac{d}{dx}\left(c\right)=0$
$\frac{d}{dx}\left(cx\right)=c\frac{d}{dx}\left(x\right)$
· Power rule for derivatives
$\frac{d}{dx}\left(x^a\right)=ax^{\left(a-1\right)}$
· Derivative of the linear function
$\frac{d}{dx}\left(x\right)=1$

Derivatives of trigonometric functions

· Derivative of the cosine function
$\frac{d}{dx}\left(\cos\left(x\right)\right)=-\sin\left(x\right)$
· Derivative of the sine function
$\frac{d}{dx}\left(\sin\left(x\right)\right)=\cos\left(x\right)$
$\lim_{x\to\:0}\left(\frac{1-\cos\left(x\right)}{x^2}\right)$

Limits

~ 0.07 s