How to find f'(x) if f of x is equal to 4 divided by the square root of x minus 2 divided by x cubed for x > 0.

Answer 1

If your equation is f(x) = 4/√(x) - 2/x³ then you would calculate the derivxative f'(x) as follows:

1) I start by writing the x's in the numerator.

4/√x is the same as 4•x^(-1/2); 2/x³ = 2•x^(-3)

so our equation would then be f(x) = 4•x^(-1/2) -2•x^(-3)

2) to find the derivative, you use the following

if f(x) = ax^b+ c, then f'(x) = a•b•x^(b-1)

so f(x) =4•x^(-1/2) - 2•x^(-3)

f'(x) = 4•(-1/2)x^{(-1/2 -1)} - 2•(-3)•x^(-3-1)

f'(x) = -2x^-(3/2) + 6x^(-4)

f'(x) = -2/sqrt(x³) + 6/x⁴

Let me know if you need more clarification..