Calculus Examples

$y = 10 + x + 10^{x}$

Step 1

Differentiate.

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Step 1.1

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

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

Step 1.2

Since $10$ is constant with respect to $x$ , the derivative of $10$ with respect to $x$ is $0$ .

$0 + \frac{d}{d x} [x] + \frac{d}{d x} [10^{x}]$

Step 1.3

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 1$ .

$0 + 1 + \frac{d}{d x} [10^{x}]$

Step 2

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

$0 + 1 + 10^{x} \ln (10)$

Step 3

Simplify.

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Step 3.1

Add $0$ and $1$ .

$1 + 10^{x} \ln (10)$

Step 3.2

Reorder terms.

$10^{x} \ln (10) + 1$