What is the derivative of e^{-x^2-5x} ?

The derivative of e^{-x^2-5x} is e^{-x^2-5x}(-2x-5)

What is the first derivative of e^{-x^2-5x} ?

The first derivative of e^{-x^2-5x} is e^{-x^2-5x}(-2x-5)

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\frac{d}{d x} (e^{- x^{2} - 5 x})

e^{- x^{2} - 5 x} (- 2 x - 5)

Solution steps

\frac{d}{d x} (e^{- x^{2} - 5 x})

Apply the chain rule:

e^{- x^{2} - 5 x} \frac{d}{d x} (- x^{2} - 5 x)

= e^{- x^{2} - 5 x} \frac{d}{d x} (- x^{2} - 5 x)

\frac{d}{d x} (- x^{2} - 5 x) = - 2 x - 5

= e^{- x^{2} - 5 x} (- 2 x - 5)

What is the derivative of e^{-x^2-5x} ?
The derivative of e^{-x^2-5x} is e^{-x^2-5x}(-2x-5)
What is the first derivative of e^{-x^2-5x} ?
The first derivative of e^{-x^2-5x} is e^{-x^2-5x}(-2x-5)