Answer:
[tex]\frac{dy}{dx}=-\frac{3}{2(1-x)}[/tex]
Step-by-step explanation:
We are given that a function
[tex]y=ln(1-x)^{\frac{3}{2}}[/tex]
We have to find the derivative of the function
[tex]y=\frac{3}{2}ln(1-x)[/tex]
By using [tex]lna^b=blna[/tex]
Differentiate w.r.t x
[tex]\frac{dy}{dx}=\frac{3}{2}\times \frac{1}{1-x}\times (-1)[/tex]
By using formula
[tex]\frac{d(lnx)}{dx}=\frac{1}{x}[/tex]
[tex]\frac{dy}{dx}=-\frac{3}{2(1-x)}[/tex]
Hence,the derivative of function
[tex]\frac{dy}{dx}=-\frac{3}{2(1-x)}[/tex]
Answer:
[tex]\frac{dy}{dx} = 3/2 [ \frac{f'x}{fx}] =3/2[ \frac{-1}{ 1-x}][/tex]
Step-by-step explanation:
we need to determine the derivative for given logrithm function
function is [tex]y = ln(1-x) \frac{3}{2}[/tex]
we knwo that
derivative of log function it form of y = ln f(x) is
[tex]\frac{dy}{dx} = \frac{f'x}{fx}[/tex]
so differentiate f'x
take u = 1- x = fx
f'x = du/dx = -1
[tex]\frac{dy}{dx} = 3/2 [ \frac{f'x}{fx}] =3/2[ \frac{-1}{ 1-x}][/tex]
