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

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

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

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

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derivative of

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

- 2 e^{- x^{2}} x

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

= - 2 e^{- x^{2}} x

y^{^{'}} = x y^{3} - x y

x^{5} - x^{3} + x, 1

\frac{d y}{d x} = cos (3 x)

\frac{\partial}{\partial x} (2 x^{3} y + 8 y^{3})

\int 4 - x^{2} d x

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