What is (\partial)/(\partial x)(2x^2y+xe^{y^2}) ?

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

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(\partial)/(\partial x)(2x^2y+xe^{y^2})

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

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

\int y + cos (x) d x

\frac{\partial}{\partial x} (\frac{7 y}{x ^{5}})

\frac{\partial}{\partial y} (ln (x^{6} + y^{4}))

\int_{0}^{2} x^{4} - 2 x^{3} d x

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