Answer:
[tex]\frac{dy}{dx} = (x+3)^{4} (7)(x-5)^{6} + (x-5)^{7} (4)(x+3)^{3}[/tex]
The values of x are x = -3 ,5 and [tex]x = \frac{-1}{11}[/tex]
Step-by-step explanation:
Step(i):-
Given that the function
y = (x+3)⁴(x-5)⁷ ...(i)
Apply UV formula
[tex]\frac{dy}{dx} = U^{l} V+ U V^{l}[/tex]
Differentiating equation (i) with respective to 'x ', we get
[tex]\frac{dy}{dx} = (x+3)^{4} (7)(x-5)^{6} + (x-5)^{7} (4)(x+3)^{3}[/tex]
Step(ii):-
Given that
[tex]\frac{dy}{dx} = 0[/tex]
[tex](x+3)^{4} (7)(x-5)^{6} + (x-5)^{7} (4)(x+3)^{3} =0[/tex]
[tex](x+3)^{3}(x-5)^{6} (7(x+3)+4(x-5))[/tex] =0
[tex](x+3)^{3}(x-5)^{6} =0 and (7(x+3)+4(x-5)) =0[/tex]
x = -3 and x=5 and 7x +21 +4x -20 =0
x = -3 and x=5 and [tex]x = \frac{-1}{11}[/tex]
