Question

Differentiating a Logarithmic Function in Exercise, find the derivative of the function. See Examples 1, 2, 3, and 4.

y = ln (1 - x)3/2

Answer 1

`(dy)/(dx) = 3/2 [ (f'x)/(fx)] =3/2[ (-1)/( 1-x)]`

Explanation:

we need to determine the derivative for given logrithm function

function is
`y = ln(1-x) (3)/(2)`

we knwo that

derivative of log function it form of y = ln f(x) is

`(dy)/(dx) = (f'x)/(fx)`

so differentiate f'x

take u = 1- x = fx

f'x = du/dx = -1

`(dy)/(dx) = 3/2 [ (f'x)/(fx)] =3/2[ (-1)/( 1-x)]`

Answer 2

`(dy)/(dx)=-(3)/(2(1-x))`

Explanation:

We are given that a function

`y=ln(1-x)^{(3)/(2)}`

We have to find the derivative of the function

`y=(3)/(2)ln(1-x)`

By using
`lna^b=blna`

Differentiate w.r.t x

`(dy)/(dx)=(3)/(2)* (1)/(1-x)* (-1)`

By using formula

`(d(lnx))/(dx)=(1)/(x)`

`(dy)/(dx)=-(3)/(2(1-x))`

Hence,the derivative of function

`(dy)/(dx)=-(3)/(2(1-x))`