What is the derivative of 8^{-3x^2} ?

The derivative of 8^{-3x^2} is -9ln(2)*2^{-9x^2+1}x

What is the first derivative of 8^{-3x^2} ?

The first derivative of 8^{-3x^2} is -9ln(2)*2^{-9x^2+1}x

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\frac{d}{d x} (8^{- 3 x^{2}})

- 9 ln (2) \cdot 2^{- 9 x^{2} + 1} x

Solution steps

\frac{d}{d x} (8^{- 3 x^{2}})

Simplify

8^{- 3 x^{2}} : 51 2^{- x^{2}}

= \frac{d}{d x} (51 2^{- x^{2}})

Apply exponent rule:

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

51 2^{- x^{2}} = e^{(- x^{2}) l n (512)}

= \frac{d}{d x} (e^{(- x^{2}) l n (512)})

Apply the chain rule:

e^{(- x^{2}) l n (512)} \frac{d}{d x} ((- x^{2}) ln (512))

= e^{(- x^{2}) l n (512)} \frac{d}{d x} ((- x^{2}) ln (512))

\frac{d}{d x} ((- x^{2}) ln (512)) = - 18 ln (2) x

= e^{(- x^{2}) l n (512)} (- 18 ln (2) x)

Simplify

e^{(- x^{2}) l n (512)} (- 18 ln (2) x) : - 9 ln (2) \cdot 2^{- 9 x^{2} + 1} x

= - 9 ln (2) \cdot 2^{- 9 x^{2} + 1} x

What is the derivative of 8^{-3x^2} ?
The derivative of 8^{-3x^2} is -9ln(2)*2^{-9x^2+1}x
What is the first derivative of 8^{-3x^2} ?
The first derivative of 8^{-3x^2} is -9ln(2)*2^{-9x^2+1}x