Am I misapplying the chain rule when differentiating $x^{5x+7}$ with respect to $x$? The problem I am attempting to solve is:
\begin{align}
y=x^{5x+7} \\
\text{Find $\frac{dy}{dx}$}
\end{align}
Here is my working so far:
$$\begin{align}
\text{let }u &= 5x+7 \\
\frac{dy}{dx}&=\frac{dy}{du} \cdot \frac{du}{dx} \\
\frac{dy}{du}&=ux^{u-1}=(5x+7)x^{5x+6} \\
\frac{du}{dx}&=5 \\
\therefore \frac{dy}{dx}&=(25x+35)x^{5x+6}
\end{align}$$
(Additionally, I'm having trouble using the align environment in Mathjax. This question wasn't formatted very well. If someone could give me some help in the comments, then I would be very thankful.)

It is $$\ln(y)=(5x+7)\ln(x)$$ so $$\frac{y'}{y}=5\ln(x)+\frac{5x+7}{x}$$
