Derivative!!!!!!!!!!!!!!!!!!!!!!!

Question

derivitave of y= (-4)/(9x^4+8)^5

Answer 1

Given that y = -4 / (9x^4 + 8)^5

Differentiating on both sides we get,

dy/dx = d/dx (-4 / (9x^4 + 8)^5 )

This in the form of d/dx(u/v) = (vdu/dx - udv/dx) / v^2

= [ (9x^4 + 8)^5 d/dx(-4) - (-4) d/dx(9x^4 + 8)^5 ] / ((9x^4 + 8)^5)^2

= [(9x^4 + 8)^5) (0) + 4 ( 5(9x^4 + 8)^4 d/dx(9x^4 + 8) )] / (9x^4 + 8)^10

                                                                            [Since d/dx(a)=0, d/dx(x^n)=nx^(n-1)]

= [0 + 20(9x^4 + 8)^4 (36x^3 + 0)] / (9x^4 + 8)^10          [Since d/dx(x^n) = nx^(n-1)]

= 720x^3(9x^4 + 8)^4  / (9x^4 + 8)^10

= 720x^3(9x^4 + 8)^4-10                                         [Since x^a/x^b = x^(a-b)]

= 720x^3(9x^4 + 8)^-6

= 720x^3 / (9x^4 + 8)^6

Therefore dy/dx = 720x^3 / (9x^4 + 8)^6