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Popular >

derivative of (3-4xe^{-2x^2})

Solution

\frac{d}{d x} ((3 - 4 x) e^{- 2 x^{2}})

Solution

- 4 e^{- 2 x^{2}} - 4 e^{- 2 x^{2}} x (3 - 4 x)

Solution steps

\frac{d}{d x} ((3 - 4 x) e^{- 2 x^{2}})

Apply the Product Rule:

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

f = 3 - 4 x, g = e^{- 2 x^{2}}

= \frac{d}{d x} (3 - 4 x) e^{- 2 x^{2}} + \frac{d}{d x} (e^{- 2 x^{2}}) (3 - 4 x)

\frac{d}{d x} (3 - 4 x) = - 4

\frac{d}{d x} (e^{- 2 x^{2}}) = - 4 e^{- 2 x^{2}} x

= (- 4) e^{- 2 x^{2}} + (- 4 e^{- 2 x^{2}} x) (3 - 4 x)

Simplify

= - 4 e^{- 2 x^{2}} - 4 e^{- 2 x^{2}} x (3 - 4 x)

Graph

Popular Examples

derivative of (x^3-3x^2+4x-5/(x^2))

\frac{d}{d x} (\frac{x ^{3} - 3 x ^{2} + 4 x - 5}{x ^{2}})

limit as x approaches-infinity of 8^x

x \to - \infty lim (8^{x})

limit as n approaches infinity of (((n+1)^3))/(5^{n+1)}

n \to \infty lim \frac{( ( n + 1 ) ^{3} )}{5 ^{n + 1}}

x^2y^{''}+5xy^'+3y=0

x^{2} y^{^{''}} + 5 x y^{^{'}} + 3 y = 0

derivative of x^{\sqrt[8]{x}}

\frac{d}{d x} (x^{8 x})

Frequently Asked Questions (FAQ)

What is the derivative of (3-4xe^{-2x^2}) ?
The derivative of (3-4xe^{-2x^2}) is -4e^{-2x^2}-4e^{-2x^2}x(3-4x)
What is the first derivative of (3-4xe^{-2x^2}) ?
The first derivative of (3-4xe^{-2x^2}) is -4e^{-2x^2}-4e^{-2x^2}x(3-4x)