What is the first d/(dy)(e^{xy}) ?

The first d/(dy)(e^{xy}) is e^{xy}x

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d/(dy)(e^{xy})

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

e^{x y} x

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

\frac{d}{d y} (x y) = x

= e^{x y} x

\int_{0}^{\frac{π}{2}} 3 cos^{5} (x) d x

\frac{d}{d x} (x^{\frac{1}{4}} - 4 e^{x})

sin^{7} (θ)

\frac{6}{s} + 16 (\frac{1}{s ^{2} + 16})

\frac{\partial}{\partial y} (x x^{2} + y^{2})