Calculus Examples

x tan (x)

$x \tan (x)$

Step 1

Differentiate using the Product Rule which states that

\frac{d}{d x} [f (x) g (x)]

$\frac{d}{d x} [f (x) g (x)]$ is

f (x) \frac{d}{d x} [g (x)] + g (x) \frac{d}{d x} [f (x)]

$f (x) \frac{d}{d x} [g (x)] + g (x) \frac{d}{d x} [f (x)]$ where

f (x) = x

$f (x) = x$ and

g (x) = tan (x)

$g (x) = \tan (x)$ .

x \frac{d}{d x} [tan (x)] + tan (x) \frac{d}{d x} [x]

$x \frac{d}{d x} [\tan (x)] + \tan (x) \frac{d}{d x} [x]$

Step 2

The derivative of

tan (x)

$\tan (x)$ with respect to

x

$x$ is

{sec}^{2} (x)

$\sec^{2} (x)$ .

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

$x \sec^{2} (x) + \tan (x) \frac{d}{d x} [x]$

Step 3

Differentiate using the Power Rule.

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Step 3.1

Differentiate using the Power Rule which states that

\frac{d}{d x} [x^{n}]

$\frac{d}{d x} [x^{n}]$ is

n x^{n - 1}

$n x^{n - 1}$ where

n = 1

$n = 1$ .

x {sec}^{2} (x) + tan (x) \cdot 1

$x \sec^{2} (x) + \tan (x) \cdot 1$

Step 3.2

Multiply

tan (x)

$\tan (x)$ by

1

$1$ .

x {sec}^{2} (x) + tan (x)

$x \sec^{2} (x) + \tan (x)$

x {sec}^{2} (x) + tan (x)

$x \sec^{2} (x) + \tan (x)$

$x \tan (x)$

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