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Popular Calculus >

derivative of-xe^{2x}

Solution

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

Solution

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of-xe^{2x} ?
The derivative of-xe^{2x} is -e^{2x}-2e^{2x}x
What is the first derivative of-xe^{2x} ?
The first derivative of-xe^{2x} is -e^{2x}-2e^{2x}x