# Partial implicit differentiation question help - Solved

I doing some multivariable calculus work and was struggling with the following question.

Given: $$e^{7z} = xyz$$ The task is to compute the partial derivatives dz/dx and dz/dy using implicit differentiation. My solution is now as follows: $$(dz/dx) 7e^{7z} = yz + (dz/dx)xy$$ And so, $$(dz/dx) (7e^{7z}-xy) = yz$$ Therefore correct answer is, $$\frac{dz}{dx} = \frac{yz}{(7e^{7z}-xy)}$$

• you need to think of $z = z(x,y)$ for this problem since apparently the problem assumes you should take $x,y$ as the independent variables. Oct 5, 2015 at 13:22

Since there are three variables so it will be differentiated by product rule i.e. $\frac{dz}{dx}7e^{7z}= yz+ \frac{dy}{dx}xz+ \frac{dz}{dx}xy$
• precisely the problem. Both $z$ and $x$ are functions of $x$. Oct 5, 2015 at 13:22