What is the derivative of 8/(9t^6) ?

The derivative of 8/(9t^6) is -(16)/(3t^7)

What is the first derivative of 8/(9t^6) ?

The first derivative of 8/(9t^6) is -(16)/(3t^7)

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derivative of

\frac{8}{9 t ^{6}}

- \frac{16}{3 t ^{7}}

Solution steps

\frac{d}{d t} (\frac{8}{9 t ^{6}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{8}{9} \frac{d}{d t} (\frac{1}{t ^{6}})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= \frac{8}{9} \frac{d}{d t} (t^{- 6})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= \frac{8}{9} (- 6 t^{- 6 - 1})

Simplify

\frac{8}{9} (- 6 t^{- 6 - 1}) : - \frac{16}{3 t ^{7}}

= - \frac{16}{3 t ^{7}}

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What is the derivative of 8/(9t^6) ?
The derivative of 8/(9t^6) is -(16)/(3t^7)
What is the first derivative of 8/(9t^6) ?
The first derivative of 8/(9t^6) is -(16)/(3t^7)