Calculus Examples

y = 19^{x}

$y = 19^{x}$

Step 1

Differentiate both sides of the equation.

\frac{d}{d x} (y) = \frac{d}{d x} (19^{x})

$\frac{d}{d x} (y) = \frac{d}{d x} (19^{x})$

Step 2

The derivative of

y

$y$ with respect to

x

$x$ is

$y'$ .

$y'$

Step 3

Differentiate using the Exponential Rule which states that

$\frac{d}{d x} [a^{x}]$ is

$a^{x} \ln (a)$ where

$a$ =

$19$ .

$19^{x} \ln (19)$

Step 4

Reform the equation by setting the left side equal to the right side.

$y' = 19^{x} \ln (19)$

Step 5

Replace

$y'$ with

$\frac{d y}{d x}$ .

$\frac{d y}{d x} = 19^{x} \ln (19)$