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Popular >

derivative of e^x(x-2)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

Popular Examples

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x \to 0 + lim ((1 + x)^{\frac{3}{x}})

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\int_{1}^{6} f (\frac{1}{2} x) d x

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\frac{d}{d x} (\frac{( 3 x ^{2} - 2 x - 3 )}{( x ^{2} + 1 ) ^{2}})

Frequently Asked Questions (FAQ)

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