Calculus Examples

y = e^{x}

$y = e^{x}$

Step 1

Differentiate both sides of the equation.

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

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

Step 2

The derivative of

y

$y$ with respect to

x

$x$ is

y'

$y'$ .

y'

$y'$

Step 3

Differentiate using the Exponential Rule which states that

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

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

a^{x} \ln (a)

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

a

$a$ =

e

$e$ .

e^{x}

$e^{x}$

Step 4

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

y' = e^{x}

$y' = e^{x}$

Step 5

Replace

y'

$y'$ with

\frac{d y}{d x}

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

\frac{d y}{d x} = e^{x}

$\frac{d y}{d x} = e^{x}$

y = e^{x}

$y = e^{x}$

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