Question

Can someone please help to differentiate this?​

Answer 1

Answer:

  $\frac{dy}{dx} = (x+3)^{4} (7)(x-5)^{6} + (x-5)^{7} (4)(x+3)^{3}$

The values of  x are x = -3 ,5   and $x = \frac{-1}{11}$

Step-by-step explanation:

Step(i):-

Given that the function

                      y = (x+3)⁴(x-5)⁷ ...(i)

Apply UV formula

$\frac{dy}{dx} = U^{l} V+ U V^{l}$

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

                 $\frac{dy}{dx} = (x+3)^{4} (7)(x-5)^{6} + (x-5)^{7} (4)(x+3)^{3}$

Step(ii):-

Given that

        $\frac{dy}{dx} = 0$

$(x+3)^{4} (7)(x-5)^{6} + (x-5)^{7} (4)(x+3)^{3} =0$

$(x+3)^{3}(x-5)^{6} (7(x+3)+4(x-5))$  =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   $x = \frac{-1}{11}$