Question

Differentiate the following functions (x^3+1)(x-2)÷x^2​

Answer 1

Given:

The given function is:

`((x^3+1)(x-2))/(x^2)`

To find:

The differentiation of the given function.

Solution:

Consider the given function,

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

It can be written as:

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

`y=(x^4-2x^3+x-2)/(x^2)`

`y=(x^4)/(x^2)-(2x^3)/(x^2)+(x)/(x^2)-(2)/(x^2)`

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

Differentiate with respect to x.

`y'=(d)/(dx)(x^2)-(d)/(dx)(2x)+(d)/(dx)(x^(-1))-(d)/(dx)\2(x^(-2))`

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

`y'=2x-2-(1)/(x^2)+(4)/(x^3)`

Therefore, the differentiation of the given function is
`2x-2-(1)/(x^2)+(4)/(x^3)`.