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Popular >

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

Solution

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

Solution

\frac{e ^{x^{2} - 2 x} ( x - 1 )}{x ^{2} - 2 x}

Solution steps

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

Apply the chain rule:

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

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

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

= e^{x^{2} - 2 x} \frac{x - 1}{x ^{2} - 2 x}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Popular Examples

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sum from n=0 to infinity of 1/(4^n)

n = 0 \sum \infty \frac{1}{4 ^{n}}

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x \to 3 lim (f (x) (x - 1))

Frequently Asked Questions (FAQ)

What is the derivative of e^{sqrt(x^2-2x)} ?
The derivative of e^{sqrt(x^2-2x)} is (e^{sqrt(x^2-2x)}(x-1))/(sqrt(x^2-2x))
What is the first derivative of e^{sqrt(x^2-2x)} ?
The first derivative of e^{sqrt(x^2-2x)} is (e^{sqrt(x^2-2x)}(x-1))/(sqrt(x^2-2x))