Differentiate z = e^(3y^2+5) with respect to y. (Hint: use chain rule.)

We can find dz/dy using chain rule dz/dy=dz/du x du/dy (1) by defining u=3y^2+5 (since the exponent of e is a function of y we call this function u) and rewrite z=e^u. Then, we find dz/du=e^u (2) and du/dy=6y (3). Now we can substitute (2) and (3) into (1) to find dz/dy=e^u 6y =6y e^(3y^2+5), where in the last line we substitute u=3y^2+5. (Ensure that you give your answer in terms of y.)