What is (\partial)/(\partial x)(cos(xy)e^{y^2}) ?

The answer to (\partial)/(\partial x)(cos(xy)e^{y^2}) is -e^{y^2}ysin(xy)

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(\partial)/(\partial x)(cos(xy)e^{y^2})

\frac{\partial}{\partial x} (cos (x y) e^{y^{2}})

- e^{y^{2}} y sin (x y)

Solution steps

\frac{\partial}{\partial x} (cos (x y) e^{y^{2}})

Treat

y

as a constant

Take the constant out:

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

= e^{y^{2}} \frac{\partial}{\partial x} (cos (x y))

Apply the chain rule:

- sin (x y) \frac{\partial}{\partial x} (x y)

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

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

= e^{y^{2}} (- sin (x y) y)

Simplify

= - e^{y^{2}} y sin (x y)

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What is (\partial)/(\partial x)(cos(xy)e^{y^2}) ?
The answer to (\partial)/(\partial x)(cos(xy)e^{y^2}) is -e^{y^2}ysin(xy)