What is (\partial)/(\partial x)(e^{-(x-3)^2}) ?

The answer to (\partial)/(\partial x)(e^{-(x-3)^2}) is e^{-x^2+6x-9}(-2x+6)

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(\partial)/(\partial x)(e^{-(x-3)^2})

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

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

Solution steps

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

Simplify

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

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

Apply the chain rule:

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

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

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

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

\frac{d}{d y} (\frac{1}{8} y^{4} + \frac{1}{4 y ^{2}})

y = x^{2} + \frac{1}{2}, (- 7, 7)

y = - 6 x

\int (\frac{2}{x ^{3}} + x^{4}) d x

\frac{d}{d x} (ln (tan (2 x)))

What is (\partial)/(\partial x)(e^{-(x-3)^2}) ?
The answer to (\partial)/(\partial x)(e^{-(x-3)^2}) is e^{-x^2+6x-9}(-2x+6)