Calculus Examples

$f (x) = \cos (\frac{π}{2}) - \frac{π}{2} \cdot \sin (\frac{π}{2})$

Step 1

The exact value of $\cos (\frac{π}{2})$ is $0$ .

$\frac{d}{d x} [0 - \frac{π}{2} \cdot \sin (\frac{π}{2})]$

Step 2

The exact value of $\sin (\frac{π}{2})$ is $1$ .

$\frac{d}{d x} [0 - \frac{π}{2} \cdot 1]$

Step 3

Differentiate.

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Step 3.1

By the Sum Rule, the derivative of $0 - \frac{π}{2} \cdot 1$ with respect to $x$ is $\frac{d}{d x} [0] + \frac{d}{d x} [- \frac{π}{2} \cdot 1]$ .

$\frac{d}{d x} [0] + \frac{d}{d x} [- \frac{π}{2} \cdot 1]$

Step 3.2

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

$0 + \frac{d}{d x} [- \frac{π}{2} \cdot 1]$

Step 4

Evaluate $\frac{d}{d x} [- \frac{π}{2} \cdot 1]$ .

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Step 4.1

Multiply $- 1$ by $1$ .

$0 + \frac{d}{d x} [- \frac{π}{2}]$

Step 4.2

Since $- \frac{π}{2}$ is constant with respect to $x$ , the derivative of $- \frac{π}{2}$ with respect to $x$ is $0$ .

$0 + 0$

Step 5

Add $0$ and $0$ .

$0$