Question

How do you find the derivative of `((2x+1)^(5)/(x^(2)+1)^(1/2))`?

Answer 1

`:.f'(x)=(((2x+1)^5)/((x^2+1)^(1/2)))[10/(2x+1)-x/(x^2+1)]`

Explanation:

Let `f(x)=(((2x+1)^5)/((x^2+1)^(1/2)))`
`:. lnf (x)=5ln (2x+1)-1/2ln (x^2+1)`
Now differentiate with respect to `x`
`(f'(x))/(f (x))=10/(2x+1)-x/(x^2+1)`
`:.f'(x)=(((2x+1)^5)/((x^2+1)^(1/2)))[10/(2x+1)-x/(x^2+1)]`