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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = e^{x y^{2}}

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

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

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

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

\int \frac{2 x ^{2}}{9 - x ^{2}} d x

\int_{0}^{1} 2 π (2 - y) (7 - 7 y^{2}) d y

\frac{3}{4 s}

\frac{d}{d x} (sec^{2} (x^{3}))

x \to 2 lim (- x + 7)

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