# How do you find the derivative of y = (ln 2)^x?

Jan 19, 2016

First, take the natural log of both sides of the equation. Then, use implicit differentiation ...

#### Explanation:

$y = {\left(\ln 2\right)}^{x}$

$\ln y = \ln \left[{\left(\ln 2\right)}^{x}\right]$

Use the property of logs ...

lny = xln(ln 2)^

Now, implicit differentiation ...

$\left(\frac{1}{y}\right) y ' = \ln \left(\ln 2\right)$

Finally, solve for $y '$

$y ' = y \ln \left(\ln 2\right)$

$= {\left(\ln 2\right)}^{x} \ln \left(\ln 2\right)$

hope that helped