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Popular >

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}

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\int cos (2 - \frac{x}{3}) d x

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x \to - 2 lim (\frac{x - 2}{x ^{3} + 8})

(\partial)/(\partial θ)(r(θ)*sin(θ))

\frac{\partial}{\partial θ} (r (θ) \cdot sin (θ))

(\partial)/(\partial x)(xze^{xz})

\frac{\partial}{\partial x} (x z e^{x z})

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}