Question

How do you differentiate `f(x)=(12sqrt(x) + x^-4 + 5)/(x^(1/8))` using the quotient rule?

Answer 1

`(((6/sqrtx)-4x^-5)x^(1/8) - (12sqrtx+x^-4+5)*1/8x^(-7/8))/(x^(1/8))^2`

Explanation:

I would prefer to avoid the quotient rule by rewriting.

`f(x) = 12x^(3/8)+x^(-33/8)+5x^(-1/8)`

`f'(x) = 9/2x^(-5/8)-33/8x^(-41/8)-5/8x^(-9/8)`

`= 9/(2x^(5/8))-33/(8x^(41/8)) -5/(8x^(9/8))`

`= (36 x^(36/8)- 33 - 5x^(32/8))/(8x^(41/8))`

`= (36 x^(9/2)- 33 - 5x^4)/(8x^(41/8))`