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Popular Calculus >

derivative of e^{2x}(2-x)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (2 - x) = - 1

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

Simplify

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

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

Graph

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\int_{0}^{6} x 36 - x^{2} d x

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Frequently Asked Questions (FAQ)

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