What is the derivative of h(t)=6ln(t^8) ?

The derivative of h(t)=6ln(t^8) is (48)/t

What is the first derivative of h(t)=6ln(t^8) ?

The first derivative of h(t)=6ln(t^8) is (48)/t

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derivative of

h (t) = 6 ln (t^{8})

\frac{48}{t}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

\frac{1}{t ^{8}} \frac{d}{d t} (t^{8})

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

\frac{d}{d t} (t^{8}) = 8 t^{7}

= 6 \cdot \frac{1}{t ^{8}} \cdot 8 t^{7}

Simplify

6 \cdot \frac{1}{t ^{8}} \cdot 8 t^{7} : \frac{48}{t}

= \frac{48}{t}

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What is the derivative of h(t)=6ln(t^8) ?
The derivative of h(t)=6ln(t^8) is (48)/t
What is the first derivative of h(t)=6ln(t^8) ?
The first derivative of h(t)=6ln(t^8) is (48)/t