What is the derivative of 5^{-x/2} ?

The derivative of 5^{-x/2} is -(ln(5)e^{-(ln(5)x)/2})/(2)

What is the first derivative of 5^{-x/2} ?

The first derivative of 5^{-x/2} is -(ln(5)e^{-(ln(5)x)/2})/(2)

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\frac{d}{d x} (5^{- \frac{x}{2}})

- \frac{ln ( 5 ) e ^{- \frac{l n ( 5 ) x}{2}}}{2}

Solution steps

\frac{d}{d x} (5^{- \frac{x}{2}})

Apply exponent rule:

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

5^{- \frac{x}{2}} = e^{(- \frac{x}{2}) l n (5)}

= \frac{d}{d x} (e^{(- \frac{x}{2}) l n (5)})

Apply the chain rule:

e^{(- \frac{x}{2}) l n (5)} \frac{d}{d x} ((- \frac{x}{2}) ln (5))

= e^{(- \frac{x}{2}) l n (5)} \frac{d}{d x} ((- \frac{x}{2}) ln (5))

\frac{d}{d x} ((- \frac{x}{2}) ln (5)) = - \frac{ln ( 5 )}{2}

= e^{(- \frac{x}{2}) l n (5)} (- \frac{ln ( 5 )}{2})

Simplify

e^{(- \frac{x}{2}) l n (5)} (- \frac{ln ( 5 )}{2}) : - \frac{ln ( 5 ) e ^{- \frac{l n ( 5 ) x}{2}}}{2}

= - \frac{ln ( 5 ) e ^{- \frac{l n ( 5 ) x}{2}}}{2}

2 \cdot x

x \to 8 lim (7 (8 x + 5)^{3})

\int_{1}^{3} 3 d x

\int_{0}^{e} \frac{1}{x} d x

\int_{0}^{\frac{π}{3}} sin (2 x) d x

What is the derivative of 5^{-x/2} ?
The derivative of 5^{-x/2} is -(ln(5)e^{-(ln(5)x)/2})/(2)
What is the first derivative of 5^{-x/2} ?
The first derivative of 5^{-x/2} is -(ln(5)e^{-(ln(5)x)/2})/(2)