Calculus Examples

$y = \sec (x) \tan (x)$

Step 1

Differentiate using the Product Rule which states that $\frac{d}{d T} [f (T) g (T)]$ is $f (T) \frac{d}{d T} [g (T)] + g (T) \frac{d}{d T} [f (T)]$ where $f (T) = \sec (x)$ and $g (T) = \tan (x)$ .

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

Step 2

Differentiate using the Constant Rule.

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Step 2.1

Since $\tan (x)$ is constant with respect to $T$ , the derivative of $\tan (x)$ with respect to $T$ is $0$ .

$\sec (x) \cdot 0 + \tan (x) \frac{d}{d T} [\sec (x)]$

Step 2.2

Since $\sec (x)$ is constant with respect to $T$ , the derivative of $\sec (x)$ with respect to $T$ is $0$ .

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

Step 3

Combine terms.

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Step 3.1

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

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

Step 3.2

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

$0 + 0$

Step 3.3

Add $0$ and $0$ .

$0$