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

The derivative of e^{-(x-3^2}) is e^{-x^2+6x-9}(-2x+6)

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

The first derivative of e^{-(x-3^2}) is e^{-x^2+6x-9}(-2x+6)

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

e^{- x^{2} + 6 x - 9} (- 2 x + 6)

Solution steps

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

Simplify

e^{- (x - 3)^{2}} : e^{- x^{2} + 6 x - 9}

= \frac{d}{d x} (e^{- x^{2} + 6 x - 9})

Apply the chain rule:

e^{- x^{2} + 6 x - 9} \frac{d}{d x} (- x^{2} + 6 x - 9)

= e^{- x^{2} + 6 x - 9} \frac{d}{d x} (- x^{2} + 6 x - 9)

\frac{d}{d x} (- x^{2} + 6 x - 9) = - 2 x + 6

= e^{- x^{2} + 6 x - 9} (- 2 x + 6)

What is the derivative of e^{-(x-3^2}) ?
The derivative of e^{-(x-3^2}) is e^{-x^2+6x-9}(-2x+6)
What is the first derivative of e^{-(x-3^2}) ?
The first derivative of e^{-(x-3^2}) is e^{-x^2+6x-9}(-2x+6)