partial derivative of x*e^(y*z) with respect to y

Differentiate with respect to y while holding x, z constant

Let's perform the differentiation:

\frac{d}{d y} (x e^{(y z)})

Apply the differentiation rule:

\frac{d}{d x} (\exp (f)) = \frac{d}{d x} (f) \cdot \exp (f)

with f =

y z

x \cdot \frac{d}{d y} (y z) \cdot e^{(y z)}

x z e^{(y z)}

▶Derivative:

e^{(y z)} x z