Question

Find the derivative of 4x^3-7x+8 ÷ x​

Answer 1

Explanation:

If a fraction
`f(x)` is defined as

`f(x) = (g(x))/(h(x))`

then the derivative
`f'(x)` is given by

`f'(x) = (g'(x)h(x) - g(x)h'(x))/(h^2(x))`

So the derivative can be calculated as follows:

`f'(x) = (d)/(dx)\left((4x^3 - 7x + 8)/(x) \right)`

`=((12x^2 - 7)x - (4x^3 - 7x + 8))/(x^2)`

`= (12x^3 - 7x - 4x^3 + 7x - 8)/(x^2)`

`= (8x^3 - 8)/(x^2)`