What is the derivative of f(t)=ln(t^9+5) ?

The derivative of f(t)=ln(t^9+5) is (9t^8)/(t^9+5)

What is the first derivative of f(t)=ln(t^9+5) ?

The first derivative of f(t)=ln(t^9+5) is (9t^8)/(t^9+5)

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derivative

\frac{9 t ^{8}}{t ^{9} + 5}

Solution steps

\frac{d}{d t} (ln (t^{9} + 5))

Apply the chain rule:

\frac{1}{t ^{9} + 5} \frac{d}{d t} (t^{9} + 5)

= \frac{1}{t ^{9} + 5} \frac{d}{d t} (t^{9} + 5)

\frac{d}{d t} (t^{9} + 5) = 9 t^{8}

= \frac{1}{t ^{9} + 5} \cdot 9 t^{8}

Simplify

\frac{1}{t ^{9} + 5} \cdot 9 t^{8} : \frac{9 t ^{8}}{t ^{9} + 5}

= \frac{9 t ^{8}}{t ^{9} + 5}

What is the derivative of f(t)=ln(t^9+5) ?
The derivative of f(t)=ln(t^9+5) is (9t^8)/(t^9+5)
What is the first derivative of f(t)=ln(t^9+5) ?
The first derivative of f(t)=ln(t^9+5) is (9t^8)/(t^9+5)