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Popular >

derivative of 2^{-x^2}

Solution

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

Solution

- ln (2) \cdot 2^{- x^{2} + 1} x

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

Simplify

e^{(- x^{2}) l n (2)} (- 2 ln (2) x) : - ln (2) \cdot 2^{- x^{2} + 1} x

= - ln (2) \cdot 2^{- x^{2} + 1} x

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Frequently Asked Questions (FAQ)

What is the derivative of 2^{-x^2} ?
The derivative of 2^{-x^2} is -ln(2)*2^{-x^2+1}x
What is the first derivative of 2^{-x^2} ?
The first derivative of 2^{-x^2} is -ln(2)*2^{-x^2+1}x