What is the derivative of 4^{-x^2} ?

The derivative of 4^{-x^2} is -ln(2)*4^{-x^2+1}x

What is the first derivative of 4^{-x^2} ?

The first derivative of 4^{-x^2} is -ln(2)*4^{-x^2+1}x

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\frac{d}{d x} (4^{- x^{2}})

- ln (2) \cdot 4^{- x^{2} + 1} x

Solution steps

\frac{d}{d x} (4^{- x^{2}})

Apply exponent rule:

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

4^{- x^{2}} = e^{(- x^{2}) l n (4)}

= \frac{d}{d x} (e^{(- x^{2}) l n (4)})

Apply the chain rule:

e^{(- x^{2}) l n (4)} \frac{d}{d x} ((- x^{2}) ln (4))

= e^{(- x^{2}) l n (4)} \frac{d}{d x} ((- x^{2}) ln (4))

\frac{d}{d x} ((- x^{2}) ln (4)) = - 4 ln (2) x

= e^{(- x^{2}) l n (4)} (- 4 ln (2) x)

Simplify

e^{(- x^{2}) l n (4)} (- 4 ln (2) x) : - ln (2) \cdot 4^{- x^{2} + 1} x

= - ln (2) \cdot 4^{- x^{2} + 1} x

What is the derivative of 4^{-x^2} ?
The derivative of 4^{-x^2} is -ln(2)*4^{-x^2+1}x
What is the first derivative of 4^{-x^2} ?
The first derivative of 4^{-x^2} is -ln(2)*4^{-x^2+1}x