Question

What is the first derivative of the curve described by `y = 1/2root(3)(x) + 8/x + 1`?

Answer 1

First of all, we can rewrite the curve as

`y = 1/2x^(1/3) + 8x^(-1) + 1`

Differentiate using the power rule, `(x^n)' = nx^(n - 1)`.

`dy/dx = 1/3(1/2)x^(-2/3) + (-1)8x^(-2) + 0`

`dy/dx = 1/(6x^(2/3)) - 8/x^2`

Hopefully this helps!