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Popular >

derivative of 3^{-x^2}

Solution

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

Solution

- 2 ln (3) \cdot 3^{- x^{2}} x

Solution steps

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

Apply exponent rule:

a^{b} = e^{b l n (a)}

3^{- x^{2}} = e^{(- x^{2}) l n (3)}

= \frac{d}{d x} (e^{(- x^{2}) l n (3)})

Apply the chain rule:

e^{(- x^{2}) l n (3)} \frac{d}{d x} ((- x^{2}) ln (3))

= e^{(- x^{2}) l n (3)} \frac{d}{d x} ((- x^{2}) ln (3))

\frac{d}{d x} ((- x^{2}) ln (3)) = - 2 ln (3) x

= e^{(- x^{2}) l n (3)} (- 2 ln (3) x)

Simplify

e^{(- x^{2}) l n (3)} (- 2 ln (3) x) : - 2 ln (3) \cdot 3^{- x^{2}} x

= - 2 ln (3) \cdot 3^{- x^{2}} x

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Frequently Asked Questions (FAQ)

What is the derivative of 3^{-x^2} ?
The derivative of 3^{-x^2} is -2ln(3)*3^{-x^2}x
What is the first derivative of 3^{-x^2} ?
The first derivative of 3^{-x^2} is -2ln(3)*3^{-x^2}x