Calculus Examples

$f (x) = 7 - 4 e^{x}$

Step 1

Differentiate.

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Step 1.1

By the Sum Rule, the derivative of $7 - 4 e^{x}$ with respect to $x$ is $\frac{d}{d x} [7] + \frac{d}{d x} [- 4 e^{x}]$ .

$\frac{d}{d x} [7] + \frac{d}{d x} [- 4 e^{x}]$

Step 1.2

Since $7$ is constant with respect to $x$ , the derivative of $7$ with respect to $x$ is $0$ .

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

Step 2

Evaluate $\frac{d}{d x} [- 4 e^{x}]$ .

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Step 2.1

Since $- 4$ is constant with respect to $x$ , the derivative of $- 4 e^{x}$ with respect to $x$ is $- 4 \frac{d}{d x} [e^{x}]$ .

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

Step 2.2

Differentiate using the Exponential Rule which states that $\frac{d}{d x} [a^{x}]$ is $a^{x} \ln (a)$ where $a$ = $e$ .

$0 - 4 e^{x}$

Step 3

Subtract $4 e^{x}$ from $0$ .

$- 4 e^{x}$