What is (\partial)/(\partial x)(e^ysin(xy)) ?

The answer to (\partial)/(\partial x)(e^ysin(xy)) is e^ycos(xy)y

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(\partial)/(\partial x)(e^ysin(xy))

\frac{\partial}{\partial x} (e^{y} sin (x y))

e^{y} cos (x y) y

Solution steps

\frac{\partial}{\partial x} (e^{y} sin (x y))

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= e^{y} \frac{\partial}{\partial x} (sin (x y))

Apply the chain rule:

cos (x y) \frac{\partial}{\partial x} (x y)

= cos (x y) \frac{\partial}{\partial x} (x y)

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

= e^{y} cos (x y) y

What is (\partial)/(\partial x)(e^ysin(xy)) ?
The answer to (\partial)/(\partial x)(e^ysin(xy)) is e^ycos(xy)y