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Popular >

derivative of ln(t^2-2t+10)

Solution

derivative of

ln (t^{2} - 2 t + 10)

Solution

\frac{2 t - 2}{t ^{2} - 2 t + 10}

Solution steps

\frac{d}{d t} (ln (t^{2} - 2 t + 10))

Apply the chain rule:

\frac{1}{t ^{2} - 2 t + 10} \frac{d}{d t} (t^{2} - 2 t + 10)

= \frac{1}{t ^{2} - 2 t + 10} \frac{d}{d t} (t^{2} - 2 t + 10)

\frac{d}{d t} (t^{2} - 2 t + 10) = 2 t - 2

= \frac{1}{t ^{2} - 2 t + 10} (2 t - 2)

Simplify

\frac{1}{t ^{2} - 2 t + 10} (2 t - 2) : \frac{2 t - 2}{t ^{2} - 2 t + 10}

= \frac{2 t - 2}{t ^{2} - 2 t + 10}

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Frequently Asked Questions (FAQ)

What is the derivative of ln(t^2-2t+10) ?
The derivative of ln(t^2-2t+10) is (2t-2)/(t^2-2t+10)
What is the first derivative of ln(t^2-2t+10) ?
The first derivative of ln(t^2-2t+10) is (2t-2)/(t^2-2t+10)