Calculus Examples

$y = - \frac{17}{2} \cdot \cosh (x) + \frac{15}{2} \cdot \sinh (x)$

Step 1

By the Sum Rule, the derivative of $- \frac{17}{2} \cdot \cosh (x) + \frac{15}{2} \cdot \sinh (x)$ with respect to $x$ is $\frac{d}{d x} [- \frac{17}{2} \cdot \cosh (x)] + \frac{d}{d x} [\frac{15}{2} \cdot \sinh (x)]$ .

$\frac{d}{d x} [- \frac{17}{2} \cdot \cosh (x)] + \frac{d}{d x} [\frac{15}{2} \cdot \sinh (x)]$

Step 2

Evaluate $\frac{d}{d x} [- \frac{17}{2} \cdot \cosh (x)]$ .

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Step 2.1

Since $- \frac{17}{2}$ is constant with respect to $x$ , the derivative of $- \frac{17}{2} \cdot \cosh (x)$ with respect to $x$ is $- \frac{17}{2} \frac{d}{d x} [\cosh (x)]$ .

$- \frac{17}{2} \frac{d}{d x} [\cosh (x)] + \frac{d}{d x} [\frac{15}{2} \cdot \sinh (x)]$

Step 2.2

The derivative of $\cosh (x)$ with respect to $x$ is $\sinh (x)$ .

$- \frac{17}{2} \sinh (x) + \frac{d}{d x} [\frac{15}{2} \cdot \sinh (x)]$

Step 3

Evaluate $\frac{d}{d x} [\frac{15}{2} \cdot \sinh (x)]$ .

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Step 3.1

Since $\frac{15}{2}$ is constant with respect to $x$ , the derivative of $\frac{15}{2} \cdot \sinh (x)$ with respect to $x$ is $\frac{15}{2} \frac{d}{d x} [\sinh (x)]$ .

$- \frac{17}{2} \sinh (x) + \frac{15}{2} \frac{d}{d x} [\sinh (x)]$

Step 3.2

The derivative of $\sinh (x)$ with respect to $x$ is $\cosh (x)$ .

$- \frac{17}{2} \sinh (x) + \frac{15}{2} \cosh (x)$

Step 4

Simplify each term.

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Step 4.1

Combine $\sinh (x)$ and $\frac{17}{2}$ .

$- \frac{\sinh (x) \cdot 17}{2} + \frac{15}{2} \cosh (x)$

Step 4.2

Move $17$ to the left of $\sinh (x)$ .

$- \frac{17 \cdot \sinh (x)}{2} + \frac{15}{2} \cosh (x)$

Step 4.3

Combine $\frac{15}{2}$ and $\cosh (x)$ .

$- \frac{17 \sinh (x)}{2} + \frac{15 \cosh (x)}{2}$