2 small derivitive probs

[Mehgan]

Hello! I'm not sure how to differentiate these two problems--

sin(xy^2) and

a/b^1/2 (too bad you can make a square root sign on the computer!)

Thank you!

 

[Gene]

The model is d(sin(u))=cos(u)d(u) so
d(sin(xy^2))=cos(xy^2)d(xy^2)
Then use the product rule for d(xy^2)
You can get around it with
sqrt(a/b) or
a/sqrt(b)
but which do you mean?

 

[galactus]

a/b^1/2 (too bad you can't make a square root sign on the computer!)

Thank you!

You can, use LaTex. You can make all sorts of symbols with it.

\(\displaystyle \sqrt{\frac{a}{b}}\)

Click on quote at the upper right corner of the post to see how it was done. There is a tutorial in this forum.

 

[Mehgan]

Gene, it's a/(b^1/2) Thank you!!

 

[Gene]

The model is d(u/v)=(v*du-u*dv)/v² so
d(a/(b^(1/2)) =
b^(1/2)da-ad(b^(1/2))/b =
(b^(1/2)da-(a/2)b^(-1/2)*db)/b

Or you can just use the product rule on
d(a*b^(-1/2))