Remember variables have specific names and are case-sensitive.
Find the derivatives of the following functions.
a. For $f(z) = (z+4)z^3$, the derivative is $\frac{d}{dz}((z+4)z^3) = \boxed{}$
b. For $f(x) = x^2(e^x - x)$, the derivative is $\frac{d}{dx}(x^2(e^x - x)) = \boxed{}$
c. For $f(w) = e^w \ln(w)$, the derivative is $\frac{d}{dw}(e^w \ln(w)) = \boxed{}$
