how do i find the derivative of (x+y)^2=x *y

Question

how do i find the derivative of  (x+y)^2=x *y

anonymous · Answer

We need more information. Are you taking the partial derivative with respect to x or with respect to y?

anonymous · Answer

hmm it says find dy/dx

anonymous · Answer

think its y

anonymous · Answer

Implicit differentiation then. Result pending...

anonymous · Answer

think its y

anonymous · Answer

hey could u also help me with tan(X+y)=4x very much appreciated

anonymous · Answer

Do you know how to do implicit differentiation? Make the equation equal to zero for a start. Expand the bracket and simplify. Then implicitly differentiate, remembering the x terms differentiate normally and any y terms get differentiated and multiplied by (dy/dx). You will need the product rule for the xy cross product.

anonymous · Answer

oh k give me a min

anonymous · Answer

i got X^2+2xy-xy=0

anonymous · Answer

Sure thing. After those steps, you factor out the (dy/dx) term and solve for (dy/dx). You will get $$(dy/dx)=(y-2x)/(x+2y)$$

anonymous · Answer

Yep, that is the first step. Notice how 2xy-xy = xy

anonymous · Answer

ook getting it now

anonymous · Answer

oh forgot y^2 above

anonymous · Answer

2x+(x.dy/dx+y)+2y.dy/dx=0 is the implicitly derived solution, you just need to solve for dy/dx

anonymous · Answer

hey when its tan (x+y)=4x what do i d with the tan?