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

The derivative of e^{(-5x^2-2x^2}) is -14e^{-7x^2}x

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

The first derivative of e^{(-5x^2-2x^2}) is -14e^{-7x^2}x

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

- 14 e^{- 7 x^{2}} x

Solution steps

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

Simplify

e^{(- 5 x^{2} - 2 x^{2})} : e^{- 7 x^{2}}

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

Apply the chain rule:

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

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

\frac{d}{d x} (- 7 x^{2}) = - 14 x

= e^{- 7 x^{2}} (- 14 x)

Simplify

= - 14 e^{- 7 x^{2}} x

What is the derivative of e^{(-5x^2-2x^2}) ?
The derivative of e^{(-5x^2-2x^2}) is -14e^{-7x^2}x
What is the first derivative of e^{(-5x^2-2x^2}) ?
The first derivative of e^{(-5x^2-2x^2}) is -14e^{-7x^2}x