Question

Question #81db1

Answer 1

`-(10/(2x+1)+1/x)`

Explanation:

differentiate using the `color(blue)"chain rule"` on each term.

`color(red)(bar(ul(|color(white)(2/2)color(black)([d/dxln(f(x))]=1/(f(x))xxf'(x))color(white)(2/2)|)))`

`d/dx(-5ln(2x+1))=-5. 1/(2x+1).d/dx(2x+1)`

`=-10/(2x+1)`

`"and " d/dx(-ln(2x))=-1/(2x).d/dx(2x)=-1/x`

`rArr-(10/(2x+1)+1/x)" is the derivative"`