Find $dy/dx$ if $xe^{9y}+y^4\sin(4x)=e^{8x}$ If $xe^{9y}+y^4\sin(4x)=e^{8x}$ implicitly defines $y$ as a function of $x$ then what is $\displaystyle \frac{dy}{dx}$?
So far, I have made the following steps:
1) Get all parts of the equation onto one side
2) Find the derivative of the whole equation
3) This equals $9e^{9y}+y^4(4cos(4x))+4y^3(sin(4x))-8e^{8x}$
4) Now, I think I am to get 'y' by itself. However, I am not sure how to do this, since there are $y$ variables as exponents, as well as non-exponent $y$ variables.
Does anyone know how I may find the derivative of this function?
All help is appreciated.

Implicitl differentiation means that we need to treat $y$ as a function of $x$ and apply Chain Rule. You also forgot to apply Product Rule to the first term. The derivative of the first term is:
\begin{align*}
\frac{d}{dx}[xe^{9y}]
&= x\left[\frac{d}{dx}e^{9y}\right] + \left[\frac{d}{dx}x\right]e^{9y} \\
&= xe^{9y}\left[\frac{d}{dx}9y\right] + \left[1\right]e^{9y} \\
&= xe^{9y} \left[9\frac{dy}{dx}\right] + e^{9y} \\
&= 9xe^{9y}y' + e^{9y} \\
\end{align*}
Now do the same thing for the second term, then solve for $y'$.
