Question

Derivatives Polynomial

Answer 1

\[f(X)=\frac{ 2x^2+3x+2 }{ Sqrtx }\]
f'(x)=

Answer 2

Use the quotient rule. \[\left( \frac{ f }{ g} \right)\prime=\frac{ f \prime g-g \prime f }{ g ^{2}}\]

Answer 3

whre is g(x) in the question?

Answer 4

\[f(x)=2x ^{2}+3x+2 \] and \[g(x)=\sqrt{x}\] or if you prefer, you can just divide the \[x ^{1/2}\] into the numerator and you are left with a simple polynomial in x that can be differentiated term by term.

Answer 5

Oh I see.
So g(x)=sqrt(x)!

Answer 6

You should get the same result either way, but if we divide, your polynomial becomes\[2x ^{3/2}+3x ^{1/2}+2x ^{-1/2}\] So, then you can just take the derivative of each term by the power rule. Bring the power down and raise the function to one power less.

Answer 7

I am confused!

Answer 8

what is the first step?

Answer 9

If you have x^n,

Then \[\frac{ d }{ dx }x ^{n}=nx ^{n-1}\]

So look at your first term. What is it? It is 2x^(3/2), so the rules says to bring the power down, and raise it to one power less.

Answer 10

Now just apply that same rule to each of the three terms.

Answer 11

d/dx2(x^2)+d/dx3(x)+d/dx(2)

Answer 12

That would be the case if you didn't have that square root on the bottom, but since you do, I believe you should use the one I typed for you after we divided by square root of x.

Answer 13

what is the next actually process?

Answer 14

I know the fact that I have to bring numbers in front of x ? :/

Answer 15

Yep, for each term with an x in it, in order to find its derivative, you have to bring the power down and raise the power to one power less

Answer 16

so 3/2*2?

Answer 17

Yes, the constants in front of each x term just get multiplied by whatever power you bring down.

Answer 18

ok, so it is 6/2?

Answer 19

Yes, then that reduces to 3.

Answer 20

OH! thats really cool.
i got it!

Answer 21

So, can I see your final answer to the derivative?

Answer 22

Ok, hold on im caculating

Answer 23

ok, is it 3x+3/2x+(-x)?

Answer 24

You forgot about the part where the exponent gets reduced by 1 power less.

Answer 25

Ok i will redo it again,

Answer 26

k

Answer 27

\[f(x)+3x ^{-1/2}+3/2x ^{1/2}+x ^{1/2}\]

Answer 28

is this right? @calmat01

Answer 29

@Dodo1 Almost. You need to substract 1 from the power of 2x^(-1/2) and bring down the power first. so the last term should be -x^(-3/2)

Answer 30

And the second term should have a negative in the exponent. It should be (3/2)x^(-1/2)