Calculus Examples

$y = \sin (t) + π \cos (t)$

Step 1

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

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

Step 2

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

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

Step 3

Evaluate $\frac{d}{d t} [π \cos (t)]$ .

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Step 3.1

Since $π$ is constant with respect to $t$ , the derivative of $π \cos (t)$ with respect to $t$ is $π \frac{d}{d t} [\cos (t)]$ .

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

Step 3.2

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

$\cos (t) + π (- \sin (t))$

Step 4

Reorder terms.

$- π \sin (t) + \cos (t)$