Calculus Examples

y = e^{x}

$y = e^{x}$

Step 1

Rewrite the equation as

e^{x} = y

$e^{x} = y$ .

e^{x} = y

$e^{x} = y$

Step 2

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

\ln (e^{x}) = \ln (y)

$\ln (e^{x}) = \ln (y)$

Step 3

Expand the left side.

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Step 3.1

Expand

\ln (e^{x})

$\ln (e^{x})$ by moving

x

$x$ outside the logarithm.

x \ln (e) = \ln (y)

$x \ln (e) = \ln (y)$

Step 3.2

The natural logarithm of

e

$e$ is

1

$1$ .

x \cdot 1 = \ln (y)

$x \cdot 1 = \ln (y)$

Step 3.3

Multiply

x

$x$ by

1

$1$ .

x = \ln (y)

$x = \ln (y)$

x = \ln (y)

$x = \ln (y)$

y = e^{x}

$y = e^{x}$

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