What is the derivative of 6^{4-x^2} ?

The derivative of 6^{4-x^2} is -ln(6)*3^{4-x^2}*2^{-x^2+5}x

What is the first derivative of 6^{4-x^2} ?

The first derivative of 6^{4-x^2} is -ln(6)*3^{4-x^2}*2^{-x^2+5}x

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derivative of

6^{4 - x^{2}}

- ln (6) \cdot 3^{4 - x^{2}} \cdot 2^{- x^{2} + 5} x

Solution steps

\frac{d}{d x} (6^{4 - x^{2}})

Apply exponent rule:

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

6^{4 - x^{2}} = e^{(4 - x^{2}) l n (6)}

= \frac{d}{d x} (e^{(4 - x^{2}) l n (6)})

Apply the chain rule:

e^{(4 - x^{2}) l n (6)} \frac{d}{d x} ((4 - x^{2}) ln (6))

= e^{(4 - x^{2}) l n (6)} \frac{d}{d x} ((4 - x^{2}) ln (6))

\frac{d}{d x} ((4 - x^{2}) ln (6)) = - 2 ln (6) x

= e^{(4 - x^{2}) l n (6)} (- 2 ln (6) x)

Simplify

e^{(4 - x^{2}) l n (6)} (- 2 ln (6) x) : - ln (6) \cdot 3^{4 - x^{2}} \cdot 2^{- x^{2} + 5} x

= - ln (6) \cdot 3^{4 - x^{2}} \cdot 2^{- x^{2} + 5} x

\frac{d}{d x} (\frac{2 - 3 x - x ^{2}}{x ^{2} - 4})

\frac{d y}{d x} = 4 e^{3 x - 4 y}

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

\frac{d}{d x} (\frac{x}{x + 5})

x \frac{d y}{d x} = y (y + 1)

What is the derivative of 6^{4-x^2} ?
The derivative of 6^{4-x^2} is -ln(6)*3^{4-x^2}*2^{-x^2+5}x
What is the first derivative of 6^{4-x^2} ?
The first derivative of 6^{4-x^2} is -ln(6)*3^{4-x^2}*2^{-x^2+5}x