Calculus Examples

$f (x) = 25 + (100 - 25 e^{- 0.5 \cdot 0})$

Step 1

Differentiate.

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Step 1.1

Multiply $- 0.5$ by $0$ .

$\frac{d}{d x} [25 + 100 - 25 e^{0}]$

Step 1.2

Anything raised to $0$ is $1$ .

$\frac{d}{d x} [25 + 100 - 25 \cdot 1]$

Step 1.3

By the Sum Rule, the derivative of $25 + 100 - 25 \cdot 1$ with respect to $x$ is $\frac{d}{d x} [25] + \frac{d}{d x} [100] + \frac{d}{d x} [- 25 \cdot 1]$ .

$\frac{d}{d x} [25] + \frac{d}{d x} [100] + \frac{d}{d x} [- 25 \cdot 1]$

Step 1.4

Since $25$ is constant with respect to $x$ , the derivative of $25$ with respect to $x$ is $0$ .

$0 + \frac{d}{d x} [100] + \frac{d}{d x} [- 25 \cdot 1]$

Step 1.5

Since $100$ is constant with respect to $x$ , the derivative of $100$ with respect to $x$ is $0$ .

$0 + 0 + \frac{d}{d x} [- 25 \cdot 1]$

Step 2

Evaluate $\frac{d}{d x} [- 25 \cdot 1]$ .

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Step 2.1

Multiply $- 25$ by $1$ .

$0 + 0 + \frac{d}{d x} [- 25]$

Step 2.2

Since $- 25$ is constant with respect to $x$ , the derivative of $- 25$ with respect to $x$ is $0$ .

$0 + 0 + 0$

Step 3

Combine terms.

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Step 3.1

Add $0$ and $0$ .

$0 + 0$

Step 3.2

Add $0$ and $0$ .

$0$