Find the derivative of the function. y=ln(frac{4x}{x-6})

Bevan Mcdonald 2021-01-04 Answered
Find the derivative of the function. y=ln(4xx6)
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Expert Answer

Asma Vang
Answered 2021-01-05 Author has 93 answers
Apply Logarithmic Properties ln(ab)=lnalnb, so
y=ln(4xx6)=ln(4x)ln(x6)
Differentiate both sides with respect to x
y=ddx[ln(4x)]ddx[ln(x6)]
Apply ddx[lnu]=uu thus
y=44x1x6
Simplify
y=1x1x6
Apply difference rule for two fractions abcd=adbcbd, to obtain
y=x6xx(x6)=6x26x
y=6x26x
Result
y=6x26x
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