Key to "Find the derivatives of the functions. r(x)=(ln⁡(x2))2" - Plainmath

hexacordoK

Answered question

2021-06-03

Find the derivatives of the functions.

r (x) = {(\ln (x^{2}))}^{2}

Answer & Explanation

l1koV

Skilled2021-06-04Added 100 answers

Using the chain rule, we get

r^{'} (x) = 2 \ln (x^{2}) {[\ln (x^{2})]}^{'}

Using the logarithm property

{\ln x}^{2} = a \ln x

, we get

\ln (x^{2}) = 2 \ln x

Thus

\frac{d}{d x} [\ln (x^{2})] = \frac{d}{d x} [2 \ln x] = \frac{2}{x}

Combine everything to get

r^{'} (x) = 2 \ln (x^{2}) \frac{2}{x} = \frac{4 \ln (x^{2})}{x}

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