Question

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

Answer 1

Answer:

$\frac{dy}{dx}=-\frac{3}{2(1-x)}$

Step-by-step explanation:

We are given that a function  

$y=ln(1-x)^{\frac{3}{2}}$

We have to find the derivative of the function  

$y=\frac{3}{2}ln(1-x)$

By using $lna^b=blna$

Differentiate w.r.t x

$\frac{dy}{dx}=\frac{3}{2}\times \frac{1}{1-x}\times (-1)$

By using formula

$\frac{d(lnx)}{dx}=\frac{1}{x}$

$\frac{dy}{dx}=-\frac{3}{2(1-x)}$

Hence,the derivative of function

$\frac{dy}{dx}=-\frac{3}{2(1-x)}$

Answer 2

Answer:

$\frac{dy}{dx} = 3/2 [ \frac{f'x}{fx}] =3/2[ \frac{-1}{ 1-x}]$

Step-by-step explanation:

we need to determine the derivative for given logrithm function

function is $y = ln(1-x) \frac{3}{2}$

we knwo that

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

$\frac{dy}{dx} = \frac{f'x}{fx}$

so differentiate f'x

take u = 1- x =  fx

f'x =  du/dx = -1

$\frac{dy}{dx} = 3/2 [ \frac{f'x}{fx}] =3/2[ \frac{-1}{ 1-x}]$