What is (\partial)/(\partial x)(x^2*e^x) ?

The answer to (\partial)/(\partial x)(x^2*e^x) is 2xe^x+e^xx^2

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(\partial)/(\partial x)(x^2*e^x)

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

y = x^{2}, y = \frac{2}{( x ^{2} + 1 )}

\int \frac{1}{x ^{2}} 2 - \frac{1}{x} d x

(19 - (15 - 2 x^{4})^{7})^{3}

(12 x^{2} + y - 1) d x - (6 y - x) d y = 0

x y^{^{'}} + 5 y = 0

What is (\partial)/(\partial x)(x^2*e^x) ?
The answer to (\partial)/(\partial x)(x^2*e^x) is 2xe^x+e^xx^2