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Popular >

derivative of 2^{-3x}

Solution

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

Solution

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

Solution steps

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

Simplify

2^{- 3 x} : 8^{- x}

= \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}

Popular Examples

integral of 1/(cot^2(8x))sec^4(8x)

\int \frac{1}{cot ^{2} ( 8 x )} sec^{4} (8 x) d x

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\int (3 x + 3) x^{2} + 2 x + 3 d x

sum from n=1 to infinity of 9-1/(n^2)

n = 1 \sum \infty 9 - \frac{1}{n ^{2}}

Frequently Asked Questions (FAQ)

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