Question

Can someone please help to differentiate this?​

Answer 1

`(dy)/(dx) = (x+3)^(4) (7)(x-5)^(6) + (x-5)^(7) (4)(x+3)^(3)`

The values of x are x = -3 ,5 and
`x = (-1)/(11)`

Explanation:

Step(i):-

Given that the function

y = (x+3)⁴(x-5)⁷ ...(i)

Apply UV formula

`(dy)/(dx) = U^(l) V+ U V^(l)`

Differentiating equation (i) with respective to 'x ', we get

`(dy)/(dx) = (x+3)^(4) (7)(x-5)^(6) + (x-5)^(7) (4)(x+3)^(3)`

Step(ii):-

Given that

`(dy)/(dx) = 0`

`(x+3)^(4) (7)(x-5)^(6) + (x-5)^(7) (4)(x+3)^(3) =0`

`(x+3)^(3)(x-5)^(6) (7(x+3)+4(x-5))` =0

`(x+3)^(3)(x-5)^(6) =0 and (7(x+3)+4(x-5)) =0`

x = -3 and x=5 and 7x +21 +4x -20 =0

x = -3 and x=5 and
`x = (-1)/(11)`