Maths
posted by Abhi on .
If tan inverse(x^2y^2/x^2+y^2)=a then prove that dy/dx=x/y (1tana/1+tana).

Hint:
write equation as:
tan(a)=(x²y²)/(x²+y²)
Cross multiply to eliminate denominators:
(x²+y²)tan(a)=(x²y²)
Implicitly differentiate both sides
(2x+2yy')tan(a) = 2x2yy'
Group terms and express y'(=dy/dx) in terms of x, y and tan(a) to get the required expression. 
Thanku soo much