Find the derivatives of the functions. r(x)=(\ln (x^{2}))^{2}

hexacordoK

hexacordoK

Answered question

2021-06-03

Find the derivatives of the functions. r(x)=(ln(x2))2

Answer & Explanation

l1koV

l1koV

Skilled2021-06-04Added 100 answers

Using the chain rule, we get
r(x)=2ln(x2)[ln(x2)]
Using the logarithm property lnx2=alnx, we get
ln(x2)=2lnx
Thus
ddx[ln(x2)]=ddx[2lnx]=2x
Combine everything to get
r(x)=2ln(x2)2x=4ln(x2)x

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