Calculus Examples

$y = 10^{x} - 5$

Step 1

By the Sum Rule, the derivative of $10^{x} - 5$ with respect to $x$ is $\frac{d}{d x} [10^{x}] + \frac{d}{d x} [- 5]$ .

$\frac{d}{d x} [10^{x}] + \frac{d}{d x} [- 5]$

Step 2

Differentiate using the Exponential Rule which states that $\frac{d}{d x} [a^{x}]$ is $a^{x} \ln (a)$ where $a$ = $10$ .

$10^{x} \ln (10) + \frac{d}{d x} [- 5]$

Step 3

Differentiate using the Constant Rule.

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Step 3.1

Since $- 5$ is constant with respect to $x$ , the derivative of $- 5$ with respect to $x$ is $0$ .

$10^{x} \ln (10) + 0$

Step 3.2

Add $10^{x} \ln (10)$ and $0$ .

$10^{x} \ln (10)$