Question

find the derivative of y with respect to x.
y = log 7e^9x
\frac{dy}{dx}=square

Explanation:

Step1: Use change - of - base formula

$y=\log_{7}e^{9x}=\frac{\ln e^{9x}}{\ln 7}$
Since $\ln e^{9x}=9x$, then $y = \frac{9x}{\ln 7}$

Step2: Differentiate with respect to x

The derivative of a function $y = ax$ (where $a=\frac{9}{\ln 7}$) with respect to $x$ is given by the power - rule $\frac{d}{dx}(ax)=a$.
$\frac{dy}{dx}=\frac{9}{\ln 7}$

Answer:

$\frac{9}{\ln 7}$