Hi
You should put into them.I mean
1-This is 2 part.First, you should put f(-1) then you should put what you found.
Solve is:f(-1)=3(-1)-2(-1)^2 so -3-2=-5 then put in other one:if f(-5):-15-50=-65
Is it correct?

4 0

2 years ago

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

Masja [62]

Given:

The given function is:

$\dfrac{(x^3+1)(x-2)}{x^2}$

To find:

The differentiation of the given function.

Solution:

Consider the given function,

$y=\dfrac{(x^3+1)(x-2)}{x^2}$

It can be written as:

$y=\dfrac{(x^3)(x)+(x^3)(-2)+(1)(x)+(1)(-2)}{x^2}$

$y=\dfrac{x^4-2x^3+x-2}{x^2}$

$y=\dfrac{x^4}{x^2}-\dfrac{2x^3}{x^2}+\dfrac{x}{x^2}-\dfrac{2}{x^2}$

$y=x^2-2x+\dfrac{1}{x}-\dfrac{2}{x^2}$

Differentiate with respect to x.

$y'=\dfrac{d}{dx}(x^2)-\dfrac{d}{dx}(2x)+\dfrac{d}{dx}(x^{-1})-\dfrac{d}{dx}\2(x^{-2})$

$y'=2x-2(1)+(-x^{-2})-2(-2x^{-3})$

$y'=2x-2-\dfrac{1}{x^2}+\dfrac{4}{x^3}$

Therefore, the differentiation of the given function is $2x-2-\dfrac{1}{x^2}+\dfrac{4}{x^3}$ .

8 0

3 years ago