Question

Find the derivative of the following function:

Answer 1

Oh good heavens just look at the time!

Answer 2

\[\frac{ 2(\sqrt[5]{x})-\sqrt[7]{x^4} }{ x^2 +3x + 1 }\]

Answer 3

you can use do the quotient rule, re-writing the rules as powers. That can be a shi(t)load of work though...

Answer 4

I mean re-writing the roots....

Answer 5

Yeah I meant to add how to do the quotient rule. I never really understood.

Answer 6

I could just give an easier question if you like

Answer 7

can you re-write the functions, so that numerator will have powers of x, instead of roots of x?

Answer 8

Sure

Answer 9

go ahead:)

Answer 10

\[\frac{ 2(x^\frac{ 1 }{ 5 }) -x^\frac{ 4 }{ 7 } }{ x^2 +3x + 1 }\]

Answer 11

don't worry about putting fractions like that, for future reference use ^{1/5} for example...

yes that is right.

Answer 12

what is the derivative of the denominator?
what is the derivative of the numerator?

Answer 13

denominator is (x^2 +3x +1)^2
What would be the numerator though. This is where I struggle the most

Answer 14

\[quotient:~~~\frac{d}{dx}~\frac{f(x)}{g(x)}=~\frac{g(x)f'(x)~-~f(x)g'(x)}{[~g(x)~]^2}\]

Answer 15

so you would need the derivative of numerator, and of denominator to find out what the top is going to be.

Answer 16

f'(x) & g'(x) is a derivative of a function notation, you know that, right?

Answer 17

sorry let me write this down, you've already written something I might have missed in class.

Answer 18

yes.

Answer 19

Okay, ill try and finish the question with the formula.

Answer 20

sure

Answer 21

\[\frac{ (\frac{ 2 }{ 5 }x^{-4/5} - \frac{ 4 }{ 7 }x^{-3/7})(x^2 +3x +1) - 2x+3(2x^{1/5} - x^{4/7}) }{ (x^2+3x+1)^2 }\]

Answer 22

that took a while haha

Answer 23

a little mistake,.

Answer 24

-(2x+3)(2x....)

Answer 25

oh yeah I missed that, its done the right way on my paper

Answer 26

very good!

Answer 27

haha thanks! I really appreciate your help! :)

Answer 28

yw