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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

y = lo g_{2} (5 x)

ln (\frac{x}{2}) 2

\int_{- 1}^{1} c (1 - x^{2}) d x

\int \frac{2 x ^{2} + 3}{x ( x - 1 ) ^{3}} d x

\frac{d y}{d x} = \frac{2 y}{x + 1}

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