Calculus Examples

$\sec (x)$

Differentiate using the chain rule, which states that $\frac{d}{d ?} [f (g (?))]$ is $f' (g (?)) g' (?)$ where $f (?) = \sec (?)$ and $g (?) = x$ .

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To apply the Chain Rule, set $u$ as $x$ .

$\frac{d}{d u} [\sec (u)] \frac{d}{d ?} [x]$

The derivative of $\sec (u)$ with respect to $u$ is $\sec (u) \tan (u)$ .

$\sec (u) \tan (u) \frac{d}{d ?} [x]$

Replace all occurrences of $u$ with $x$ .

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

Since $x$ is constant with respect to $?$ , the derivative of $x$ with respect to $?$ is $0$ .

$\sec (x) \tan (x) \cdot 0$

Combine terms.

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Multiply $0$ by $\sec (x)$ .

$0 \tan (x)$

Multiply $0$ by $\tan (x)$ .

$0$