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Popular >

derivative of (x^2+x)e^x

Solution

derivative of

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

Solution

e^{x} x^{2} + 3 e^{x} x + e^{x}

Solution steps

\frac{d}{d x} ((x^{2} + x) e^{x})

Apply the Product Rule:

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

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

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

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

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

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

Simplify

(2 x + 1) e^{x} + e^{x} (x^{2} + x) : e^{x} x^{2} + 3 e^{x} x + e^{x}

= e^{x} x^{2} + 3 e^{x} x + e^{x}

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Frequently Asked Questions (FAQ)

What is the derivative of (x^2+x)e^x ?
The derivative of (x^2+x)e^x is e^xx^2+3e^xx+e^x
What is the first derivative of (x^2+x)e^x ?
The first derivative of (x^2+x)e^x is e^xx^2+3e^xx+e^x