# Partial derivative

teng125
f(x,y)=2y / (y+cos x) .Find partial derivative w.r.t x

can someone teach me how to do this pls

thanx

## Answers and Replies

Homework Helper
If y doesn't depend on x, treat y as a constant and find the derivative wrt x as you normally do.

Staff Emeritus
Science Advisor
To do a partial derivative with respect to one variable, treat the other variables as 'constants'. In the equation given, for a partial derivative with respect to x, treat y as a constant and use the rules for ordinary differentiation.

Science Advisor
Homework Helper
Gold Member
Since you're doing multiple-variable calculus, you probably know how to differentiate the function f(x) = 2k / (k+cos x ) where k is a constant? Find that, then replace k by y and you get the partial derivative of f(x,y) wrt x.

teng125
can someone show this because i don't know how to do

Gagle The Terrible
Just Differentiate f(x) as if y was a constant. Just concentrate on the x variable, the only one that is "important" now. The derivative of the function f(x) = 2k/(k+cos x ) where k is a constant (and then changing k for y) is the same as the partial derivative of f(x,y)=2y / (y+cos x) w.r.t x.
Nothing else is to be shown.

teng125
the formula is it vu'-u'v/(v^2) ??

Homework Helper
teng125 said:
the formula is it vu'-u'v/(v^2) ??
Uhmm, nope. The red-highlighted part is wrong. It should read uv', i.e the whole formula is:
$$\left( \frac{u}{v} \right) ' = \frac{u'v - uv'}{v ^ 2}$$.
Can you go from here? :)