What is the derivative of 6^{6-x^2} ?

The derivative of 6^{6-x^2} is -ln(6)*3^{6-x^2}*2^{-x^2+7}x

What is the first derivative of 6^{6-x^2} ?

The first derivative of 6^{6-x^2} is -ln(6)*3^{6-x^2}*2^{-x^2+7}x

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\frac{d}{d x} (6^{6 - x^{2}})

- ln (6) \cdot 3^{6 - x^{2}} \cdot 2^{- x^{2} + 7} x

Solution steps

\frac{d}{d x} (6^{6 - x^{2}})

Apply exponent rule:

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

6^{6 - x^{2}} = e^{(6 - x^{2}) l n (6)}

= \frac{d}{d x} (e^{(6 - x^{2}) l n (6)})

Apply the chain rule:

e^{(6 - x^{2}) l n (6)} \frac{d}{d x} ((6 - x^{2}) ln (6))

= e^{(6 - x^{2}) l n (6)} \frac{d}{d x} ((6 - x^{2}) ln (6))

\frac{d}{d x} ((6 - x^{2}) ln (6)) = - 2 ln (6) x

= e^{(6 - x^{2}) l n (6)} (- 2 ln (6) x)

Simplify

e^{(6 - x^{2}) l n (6)} (- 2 ln (6) x) : - ln (6) \cdot 3^{6 - x^{2}} \cdot 2^{- x^{2} + 7} x

= - ln (6) \cdot 3^{6 - x^{2}} \cdot 2^{- x^{2} + 7} x

d er i v a t i v e y = - 2 x + 7

\int \frac{1}{x ^{5} 9 x ^{2} - 1} d x

\int sin (2) (x) d x

x \to 5 lim (sin (\frac{x π}{3}))

\int \frac{1}{4 - 16 x ^{2}} d x

What is the derivative of 6^{6-x^2} ?
The derivative of 6^{6-x^2} is -ln(6)*3^{6-x^2}*2^{-x^2+7}x
What is the first derivative of 6^{6-x^2} ?
The first derivative of 6^{6-x^2} is -ln(6)*3^{6-x^2}*2^{-x^2+7}x