What's the derivative of h(x)= (2x - 3 / x) ^3?

Answer 1

We can use the chain rule and the power rule to find the derivative of h(x):

h(x) = [(2x - 3) / x]^3

h'(x) = 3[(2x - 3) / x]^2 * [(d/dx)(2x - 3)/x]

To find (d/dx)(2x - 3)/x, we can use the quotient rule:

(d/dx)(2x - 3)/x = [(d/dx)(2x - 3)x - (d/dx)x(2x - 3)] / x^2

= [2x - 3 - 1(2x - 3)] / x^2

= (2 - 3/x) / x^2

Substituting this into the expression for h'(x), we get:

h'(x) = 3[(2x - 3) / x]^2 * (2 - 3/x) / x^2

= 3(2x - 3)^2(2 - 3/x) / x^5

Therefore, the derivative of h(x) is:

h'(x) = 3(2x - 3)^2(2 - 3/x) / x^5

Answer 2

h(x) = (2x-3/x)³ = (g(x))³

Be sure to use the chain rule

h'(x) = 3(g(x))²g'(x) = 3(2x-3/x)²(2+3/x²)