Differentiating equations of the type ln[f(x)]

To solve such equations we take advantage of log lawes to simplify the problem .

E.g

ln[sqrt(1-x2)] = ln[(1-x2)1/2] = 1/2ln[1-x2]

After simplifing the problem we can differentiate with respect to x 

y = 1/2ln[1-x2]

 let f(x) = 1-x2

Use the Chain rule 

dy/dx = dy/df * df/dx 

dy/df = 1/(2*f(x))

df/dx = -2x

dy/dx = - 1/2[  2x/( 1-x2  ) ]

Provides a good practice of chain rule. differentiating logarithms and properties of logs.

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Answered by Mousa S. Maths tutor

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