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)

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

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)

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)