What is (\partial)/(\partial y)(sin(xy^2+y)+2e^x) ?

The answer to (\partial)/(\partial y)(sin(xy^2+y)+2e^x) is cos(xy^2+y)(2xy+1)

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(\partial)/(\partial y)(sin(xy^2+y)+2e^x)

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

cos (x y^{2} + y) (2 x y + 1)

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial y} (sin (x y^{2} + y)) = cos (x y^{2} + y) (2 x y + 1)

\frac{\partial}{\partial y} (2 e^{x}) = 0

= cos (x y^{2} + y) (2 x y + 1) + 0

Simplify

= cos (x y^{2} + y) (2 x y + 1)

What is (\partial)/(\partial y)(sin(xy^2+y)+2e^x) ?
The answer to (\partial)/(\partial y)(sin(xy^2+y)+2e^x) is cos(xy^2+y)(2xy+1)