Question

d/dx Cos x/x^1/2

Answer 1

\[- (\sqrt{x}*sinx + \cos x)/2x \sqrt{x}\] is how far I got but it should be 2x*sinx in the denominator...

Answer 2

*numerator

Answer 3

You mean this:

\[\frac{d}{dx}(\frac{\cos(x)}{\sqrt{x}})\]

Answer 4

yep

Answer 5

No need to tell I will use Divide Rule here..

Answer 6

Divide rule? Like the quotient rule?

Answer 7

It must be 2 there..

Answer 8

Yes, quotient rule..

Answer 9

\(\sqrt{x} \cdot sin(x)\) should be multiplied by \(2\sqrt{x}\).. You forgot to do that I think..

Answer 10

\[\large \frac{d}{dx} (\frac{\cos(x)}{\sqrt{x}}) = \frac{\sqrt{x} \cdot (-\sin(x)) - \cos(x) \cdot \frac{1}{2 \sqrt{x}}}{x}\]

Answer 11

And then you will get it as:

\[\color{red}{\frac{-[2 \cdot x \cdot \sin(x) + \cos(x)]}{2 \cdot x \cdot \sqrt{x}}}\]

Answer 12

Getting or not??

Answer 13

Trying to...

Answer 14

I don't quite catch what happens in the step between the unsimplified derivative and the above function in red

Answer 15

where does the two being multiplied with the x comes from?

Answer 16

See, there is \(2\sqrt{x}\) and why are you directly taking that into denominator?? First take LCM and then send it in denominator??

Answer 17

So you multiply the denominator and the numerator by \[2\sqrt{x}\]

Answer 18

Let me ask you some other question so that you can get where you are going wrong:

Tell me its value:

\[\large \frac{1 + \frac{3}{5}}{7}\]

Answer 19

Yes, you can say that..

Answer 20

I got it! Thanks a lot! :)

Answer 21

\[\frac{\large 2 \sqrt{x}\frac{}{}[-\sqrt{x}\sin(x) - \frac{\cos(x)}{2 \sqrt{x}}]}{2x \sqrt{x}} \implies \frac{-2x \sin(x) - \cos(x)}{2x \sqrt{x}}\]

Answer 22

In your terms yes multiply by 2 root{x} with numerator and denominator, so you will get that... :)

You are welcome dear..