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Popular >

derivative of f(t)=(8^{8t})/t

Solution

derivative of

f (t) = \frac{8 ^{8 t}}{t}

Solution

\frac{e ^{8 t l n (8)} \cdot 24 ln ( 2 ) t - 1 \cdot 8 ^{8 t}}{t ^{2}}

Solution steps

\frac{d}{d t} (\frac{8 ^{8 t}}{t})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d t} ( 8 ^{8 t} ) t - \frac{d t}{d t} 8 ^{8 t}}{t ^{2}}

\frac{d}{d t} (8^{8 t}) = e^{8 t l n (8)} \cdot 24 ln (2)

\frac{d t}{d t} = 1

= \frac{e ^{8 t l n (8)} \cdot 24 ln ( 2 ) t - 1 \cdot 8 ^{8 t}}{t ^{2}}

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Frequently Asked Questions (FAQ)

What is the derivative of f(t)=(8^{8t})/t ?
The derivative of f(t)=(8^{8t})/t is (e^{8tln(8)}*24ln(2)t-1*8^{8t})/(t^2)
What is the first derivative of f(t)=(8^{8t})/t ?
The first derivative of f(t)=(8^{8t})/t is (e^{8tln(8)}*24ln(2)t-1*8^{8t})/(t^2)