Calculus Examples

$f (t) = t + \cos (t)$

Step 1

Differentiate.

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Step 1.1

By the Sum Rule, the derivative of $t + \cos (t)$ with respect to $t$ is $\frac{d}{d t} [t] + \frac{d}{d t} [\cos (t)]$ .

$\frac{d}{d t} [t] + \frac{d}{d t} [\cos (t)]$

Step 1.2

Differentiate using the Power Rule which states that $\frac{d}{d t} [t^{n}]$ is $n t^{n - 1}$ where $n = 1$ .

$1 + \frac{d}{d t} [\cos (t)]$

Step 2

The derivative of $\cos (t)$ with respect to $t$ is $- \sin (t)$ .

$1 - \sin (t)$