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Popular Calculus >

derivative of (x^2-2xe^x)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (x^{2} - 2 x) = 2 x - 2

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

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

Simplify

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

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

Graph

Popular Examples

integral of xsin(-3x)

\int x sin (- 3 x) d x

integral of ln(x^2+1)

\int ln (x^{2} + 1) d x

laplacetransform e^{2t}sin(5t)

l a pl a ce t r an s f or m e^{2 t} sin (5 t)

integral from 0 to pi/2 of-2sin^2(3x)

\int_{0}^{\frac{π}{2}} - 2 sin^{2} (3 x) d x

((dy)/(dx))=0.011*y*(2-(y-25))

(\frac{d y}{d x}) = 0.011 \cdot y \cdot (2 - (y - 25))

Frequently Asked Questions (FAQ)

What is the derivative of (x^2-2xe^x) ?
The derivative of (x^2-2xe^x) is e^xx^2-2e^x
What is the first derivative of (x^2-2xe^x) ?
The first derivative of (x^2-2xe^x) is e^xx^2-2e^x