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Popular >

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

Solution

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

Solution

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

Solution steps

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

Simplify

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

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

Apply the chain rule:

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

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

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

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

Popular Examples

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Frequently Asked Questions (FAQ)

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