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Popular Calculus >

derivative of 8^{-x}

Solution

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

Solution

- 3 ln (2) \cdot 8^{- x}

Solution steps

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

Apply exponent rule:

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

8^{- x} = e^{(- x) l n (8)}

= \frac{d}{d x} (e^{(- x) l n (8)})

Apply the chain rule:

e^{(- x) l n (8)} \frac{d}{d x} ((- x) ln (8))

= e^{(- x) l n (8)} \frac{d}{d x} ((- x) ln (8))

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

= e^{(- x) l n (8)} (- 3 ln (2))

Simplify

e^{(- x) l n (8)} (- 3 ln (2)) : - 3 ln (2) \cdot 8^{- x}

= - 3 ln (2) \cdot 8^{- x}

Graph

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Frequently Asked Questions (FAQ)

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