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Popular >

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

Solution

derivative of

\frac{e ^{x^{2}}}{e ^{x}}

Solution

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

Solution steps

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

Simplify

\frac{e ^{x^{2}}}{e ^{x}} : e^{x^{2} - x}

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

Apply the chain rule:

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

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

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

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

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Frequently Asked Questions (FAQ)

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