What is (\partial)/(\partial y)(e^{-xy^2}+y^3x^4) ?

The answer to (\partial)/(\partial y)(e^{-xy^2}+y^3x^4) is -2xe^{-xy^2}y+3x^4y^2

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(\partial)/(\partial y)(e^{-xy^2}+y^3x^4)

\frac{\partial}{\partial y} (e^{- x y^{2}} + y^{3} x^{4})

- 2 x e^{- x y^{2}} y + 3 x^{4} y^{2}

Solution steps

\frac{\partial}{\partial y} (e^{- x y^{2}} + y^{3} x^{4})

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (e^{- x y^{2}}) + \frac{\partial}{\partial y} (y^{3} x^{4})

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

\frac{\partial}{\partial y} (y^{3} x^{4}) = 3 x^{4} y^{2}

= - 2 x e^{- x y^{2}} y + 3 x^{4} y^{2}

What is (\partial)/(\partial y)(e^{-xy^2}+y^3x^4) ?
The answer to (\partial)/(\partial y)(e^{-xy^2}+y^3x^4) is -2xe^{-xy^2}y+3x^4y^2