Question

use the quotient rule.
xsinx+cosx
Plz hlp.

Answer 1

derivative or integrate?

Answer 2

derivative

Answer 3

why would you use quotient rule?

Answer 4

thats a product rule

Answer 5

noooooo idea, that's what it says on my homework :/

Answer 6

you ned to use the product rule,
is an easy one
\[\frac{ d }{ dx}\ xsinx + \frac{ d }{ dx} cosx\]
note : \[\[\frac{ d }{ dx}[f(x).g(x)] = f(x) \times \frac{ d }{ dx}g(x) + g(x) \times \frac{ d }{ dx}f(x)\]

Answer 7

yeah I know how to use the product rule, it just tripped me out that the directions ask for the quotient rule. thank you.

Answer 8

Suggestion: A product can be re-written as a quotient, thus enabling the use of the quotient rule as the given problem requires.

Answer 9

how would you do that?

Answer 10

good catch Hero, but thats just pain to use it when the problem is clearly product rule, weird.

Answer 11

It's a pain, however, I can remember all sorts of problems that could be solved using much simpler methods, yet they asked and required that I do them using very specific, well defined and established methods that were seemingly written in stone with regard to which I could not object.

Answer 12

so i just use product rule?

Answer 13

ya you need to use the product rule ;)

Answer 14

In my humble opinion, I highly recommend that you do it using the quotient rule.

Answer 15

I have no idea how to do that though.

Answer 16

Write g(x) as the denominator the fraction

Answer 17

its better you use product rule, in product rule , you will get the answer in 2 steps whereas you need to solve many steps in order to solve using the quotient rule :O

Answer 18

ok, so it would be xsinx/cosx?

Answer 19

No, it wouldn't be that, because then you would be changing an addition into a division which is not allowed under any circumstance.

Answer 20

If you were to use the product rule, what would you choose for f(x) and g(x)

Answer 21

Whatever you would choose for g(x), write that as the denominator of your fraction.

Answer 22

xsinx for f and cosx for g?

Answer 23

So you're going to apply the product rule to an addition?

Answer 24

can you explain what f and g would be and why? I've never done that before.

Answer 25

okay
f(x)= x g(x) = y
if you find the derivative of f(x) it is '1'
and the derivatiove of g(x)= y = 'dy/dx'
now you can substitute the values in the formula i mentioned above ;)

Answer 26

@lizlozada, you mean to tell me it isn't obvious what the product is ? And that when using the product rule, the first thing being multiplied would be f(x) and the second thing being multiplied with the first would g(x)?

Answer 27

\[f(x) = x , \frac{ d }{ dx }f(x) = 1, g(x)= \sin x , \frac{ d }{ dx }\sin x= \cos x\]

Answer 28

no, never mind, I'll ask my teacher tomorrow, thanks for your help.

Answer 29

thats the differentiation of xsinx
and you can differentiate cosx easily ;)
so here you get the answer ;)

Answer 30

\[(x \times cosx + sinx \times 1 )- (sinx)\]
hence you can solve further ;)