Calculus Examples

$f (x) = \ln (2) - 2^{2}$

Step 1

Differentiate.

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Step 1.1

Raise $2$ to the power of $2$ .

$\frac{d}{d x} [\ln (2) - 1 \cdot 4]$

Step 1.2

By the Sum Rule, the derivative of $\ln (2) - 1 \cdot 4$ with respect to $x$ is $\frac{d}{d x} [\ln (2)] + \frac{d}{d x} [- 1 \cdot 4]$ .

$\frac{d}{d x} [\ln (2)] + \frac{d}{d x} [- 1 \cdot 4]$

Step 1.3

Since $\ln (2)$ is constant with respect to $x$ , the derivative of $\ln (2)$ with respect to $x$ is $0$ .

$0 + \frac{d}{d x} [- 1 \cdot 4]$

Step 2

Evaluate $\frac{d}{d x} [- 1 \cdot 4]$ .

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Step 2.1

Multiply $- 1$ by $4$ .

$0 + \frac{d}{d x} [- 4]$

Step 2.2

Since $- 4$ is constant with respect to $x$ , the derivative of $- 4$ with respect to $x$ is $0$ .

$0 + 0$

Step 3

Add $0$ and $0$ .

$0$