Calculus Examples

$y = \arccos (s) (x) + b \sin (x)$

Step 1

By the Sum Rule, the derivative of $\arccos (s) (x) + b \sin (x)$ with respect to $x$ is $\frac{d}{d x} [\arccos (s) (x)] + \frac{d}{d x} [b \sin (x)]$ .

$\frac{d}{d x} [\arccos (s) (x)] + \frac{d}{d x} [b \sin (x)]$

Step 2

Evaluate $\frac{d}{d x} [\arccos (s) (x)]$ .

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Step 2.1

Since $\arccos (s)$ is constant with respect to $x$ , the derivative of $\arccos (s) x$ with respect to $x$ is $\arccos (s) \frac{d}{d x} [x]$ .

$\arccos (s) \frac{d}{d x} [x] + \frac{d}{d x} [b \sin (x)]$

Step 2.2

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 1$ .

$\arccos (s) \cdot 1 + \frac{d}{d x} [b \sin (x)]$

Step 2.3

Multiply $\arccos (s)$ by $1$ .

$\arccos (s) + \frac{d}{d x} [b \sin (x)]$

Step 3

Evaluate $\frac{d}{d x} [b \sin (x)]$ .

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Step 3.1

Since $b$ is constant with respect to $x$ , the derivative of $b \sin (x)$ with respect to $x$ is $b \frac{d}{d x} [\sin (x)]$ .

$\arccos (s) + b \frac{d}{d x} [\sin (x)]$

Step 3.2

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

$\arccos (s) + b \cos (x)$

Step 4

Reorder terms.

$b \cos (x) + \arccos (s)$