What is (\partial)/(\partial x)((x-1)^2e^x) ?

The answer to (\partial)/(\partial x)((x-1)^2e^x) is e^xx^2-e^x

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(\partial)/(\partial x)((x-1)^2e^x)

\frac{\partial}{\partial x} ((x - 1)^{2} e^{x})

e^{x} x^{2} - e^{x}

Solution steps

\frac{\partial}{\partial x} ((x - 1)^{2} e^{x})

Apply the Product Rule:

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

f = (x - 1)^{2}, g = e^{x}

= \frac{\partial}{\partial x} ((x - 1)^{2}) e^{x} + \frac{\partial}{\partial x} (e^{x}) (x - 1)^{2}

\frac{\partial}{\partial x} ((x - 1)^{2}) = 2 (x - 1)

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

= 2 (x - 1) e^{x} + e^{x} (x - 1)^{2}

Simplify

2 (x - 1) e^{x} + e^{x} (x - 1)^{2} : e^{x} x^{2} - e^{x}

= e^{x} x^{2} - e^{x}

\frac{d}{d x} (\frac{132}{x ^{13}})

\int_{0}^{\infty} 3 x e^{- 3 x} d x

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

\int \frac{x + 6}{x} d x

y = 4 x + 9, (4, 5)

What is (\partial)/(\partial x)((x-1)^2e^x) ?
The answer to (\partial)/(\partial x)((x-1)^2e^x) is e^xx^2-e^x