Thread: partial derivative

What is the partial derivative with respect to x of

arctan(x/y)?

I know the derivative of arctan(x) is 1/(1-(x.x))
does this help?

Originally Posted by syster

What is the partial derivative with respect to x of

arctan(x/y)?

I know the derivative of arctan(x) is 1/(1-(x.x))
does this help?

Hi

Just consider y as a constant
BTW the derivative of arctan(x) is 1/(1+x²)

Yes it helps

Originally Posted by syster

What is the partial derivative with respect to x of

arctan(x/y)?

I know the derivative of arctan(x) is 1/(1+(x.x))
does this help?

Apply the chain rule of differentiation.

We know that [u(v(x))]'=v'(x) u'(v(x))

Here, u=arctan and v(x)=x/y

so the derivative of arctan(x/y)=(1/y)/(1+(x/y)^2)

thanks
mistake with the minus instead to the plus just hit the wrong button