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Popular >

derivative of 2e^{-4x^2+3x+7}

Solution

\frac{d}{d x} (2 e^{- 4 x^{2} + 3 x + 7})

Solution

2 e^{- 4 x^{2} + 3 x + 7} (- 8 x + 3)

Solution steps

\frac{d}{d x} (2 e^{- 4 x^{2} + 3 x + 7})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (e^{- 4 x^{2} + 3 x + 7})

Apply the chain rule:

e^{- 4 x^{2} + 3 x + 7} \frac{d}{d x} (- 4 x^{2} + 3 x + 7)

= e^{- 4 x^{2} + 3 x + 7} \frac{d}{d x} (- 4 x^{2} + 3 x + 7)

\frac{d}{d x} (- 4 x^{2} + 3 x + 7) = - 8 x + 3

= 2 e^{- 4 x^{2} + 3 x + 7} (- 8 x + 3)

Popular Examples

derivative of f(x)= 7/(sqrt(t))derivative of

f (x) = \frac{7}{t}

derivative of ln((4x/(x+9)))

\frac{d}{d x} (ln (\frac{4 x}{x + 9}))

integral from 0 to 2 of sqrt(1+9x)

\int_{0}^{2} 1 + 9 x d x

integral from 6 to 9 of 1/(9+(x-6)^2)

\int_{6}^{9} \frac{1}{9 + ( x - 6 ) ^{2}} d x

derivative of x+c

\frac{d}{d x} (x + c)

Frequently Asked Questions (FAQ)

What is the derivative of 2e^{-4x^2+3x+7} ?
The derivative of 2e^{-4x^2+3x+7} is 2e^{-4x^2+3x+7}(-8x+3)
What is the first derivative of 2e^{-4x^2+3x+7} ?
The first derivative of 2e^{-4x^2+3x+7} is 2e^{-4x^2+3x+7}(-8x+3)