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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{- x^{2}}, g = - 2 x

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

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

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

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

Simplify

(- 2 e^{- x^{2}} x) (- 2 x) + (- 2) e^{- x^{2}} : 4 e^{- x^{2}} x^{2} - 2 e^{- x^{2}}

= 4 e^{- x^{2}} x^{2} - 2 e^{- x^{2}}

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y^{''}+y=-sin(2x),y(0)=0,y^'(0)=0

y^{^{''}} + y = - sin (2 x), y (0) = 0, y^{^{'}} (0) = 0

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\int \frac{( 9 + x + x ^{2} )}{x} d x

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Frequently Asked Questions (FAQ)

What is the derivative of (e^{-x^2}(-2x)) ?
The derivative of (e^{-x^2}(-2x)) is 4e^{-x^2}x^2-2e^{-x^2}
What is the first derivative of (e^{-x^2}(-2x)) ?
The first derivative of (e^{-x^2}(-2x)) is 4e^{-x^2}x^2-2e^{-x^2}