What is (\partial)/(\partial x)((x^2-8)e^x) ?

The answer to (\partial)/(\partial x)((x^2-8)e^x) is 2xe^x+e^x(x^2-8)

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(\partial)/(\partial x)((x^2-8)e^x)

\frac{\partial}{\partial x} ((x^{2} - 8) e^{x})

2 x e^{x} + e^{x} (x^{2} - 8)

Solution steps

\frac{\partial}{\partial x} ((x^{2} - 8) e^{x})

Apply the Product Rule:

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

f = x^{2} - 8, g = e^{x}

= \frac{\partial}{\partial x} (x^{2} - 8) e^{x} + \frac{\partial}{\partial x} (e^{x}) (x^{2} - 8)

\frac{\partial}{\partial x} (x^{2} - 8) = 2 x

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

= 2 x e^{x} + e^{x} (x^{2} - 8)

\frac{\partial}{\partial u} (\frac{v}{6 + uv w})

\int_{0}^{3} x 9 - x^{2} d x

\frac{d}{d x} (8 x - 2 x^{3})

\int x^{3} x^{4} + 2 d x

(3 - 5 x e^{x}) (3 x + 2)

What is (\partial)/(\partial x)((x^2-8)e^x) ?
The answer to (\partial)/(\partial x)((x^2-8)e^x) is 2xe^x+e^x(x^2-8)