if y=(x^3-2/2x^5-1)^4 find dy/dx at x=1

Question

work out the problem please

Answer 1

y = ( (x^3 - 2) / (2x^5 - 1) ) ^4

dy/dx = 4 * ( ( (x^3 - 2) / (2x^5 - 1) ) ^3 ) * ( (2x^5 - 1)(3x^2)  - (x^3 - 2)(10x^4) ) / (2x^5 - 1)^2

At x = 1:

dy/dx = 4 * ( ( (1^3 - 2) / (2(1^5) - 1) ) ^3 ) * ( (2(1^5) - 1)(3(1^2))  - ((1^3) - 2)(10(1^4)) ) / (2(1^5) - 1)^2

dy/dx = 4 * ( ( (1 - 2) / (2(1) - 1) ) ^3 ) * ( (2(1) - 1)(3(1))  - ((1) - 2)(10(1)) ) / (2(1) - 1)^2

dy/dx = 4 * ( ( (-1) / (2 - 1) ) ^3 ) * ( (2 - 1)(3)  - (1 - 2)(10) ) / (2 - 1)^2

dy/dx = 4 * ( ( (-1) / (-1) ) ^3 ) * ( (-1)(3)  - (-1)(10) ) / (-1)^2

dy/dx = 4 * ( (1) ^3 ) * ( -3  +10 ) / 1

dy/dx = 4 * (1) * (7)

dy/dx = 28