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

The derivative of 4^{-x/4} is -(ln(2)e^{-(ln(2)x)/2})/(2)

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

The first derivative of 4^{-x/4} is -(ln(2)e^{-(ln(2)x)/2})/(2)

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

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{4 x ^{2} - 3}{8 x ^{3} + 1}

\frac{d}{d x} (\frac{x cos ( π x ) + 1}{1 - x})

\frac{s + 1}{s ^{2} + 2}

(y - x 2) d x + (x + y 2) d y = 0

\int (\frac{- 4}{x}) d x

What is the derivative of 4^{-x/4} ?
The derivative of 4^{-x/4} is -(ln(2)e^{-(ln(2)x)/2})/(2)
What is the first derivative of 4^{-x/4} ?
The first derivative of 4^{-x/4} is -(ln(2)e^{-(ln(2)x)/2})/(2)