Implicit Differentiation regarding sin and cos

[Vader07]

Hey everybody,


I am doing these implicit differenitation problems but I got a detour on these two:

For the 1st one
Find d/dx at the point (1,0) on the curve implicitly defined by

sin (Pi x^2 + y) = xy

For the 2nd one
Find d/dx at the point (3/2, 3) on the curve implicitly defined by

cos (Pi x y) = cos (Pi(x + y)


regarding the first one this is what I got cos (Pi x ^2)(d/dx)(x^2) + sin (Pi x^2) + cos y + sin y
I am on the right track or is this completely wrong

Any help would greatly appreciated. Thanks in advance

 

[arthur ohlsten]

1) sin[pix^2+y] = xy take derivative with respect to x
cos(pix^2+y)[2pix+dy/dx] = xdy/dx+y
at x=1 y=0
cospi [ 2pi+dy/dx]=dy/dx but cos pi = -1
-2 pi - dy/dx =dy/dx
dy/dx= -pi answer
==========================================================
2)
cos(pixy)= cos[pi(x+y)] take derivative
- sin(pixy) [pi[x dy/dx+y]]=-sin[pi(x+y)] [pi+pidy/dx]
at 3/2,3
sin(9/2 pi) [ 3pi/2 dy/dx +3pi] = sin (pi9/2) [pi+pi dy/dx
3pi /2 dy/dx +3pi = pi + pi dy/dx divide by pi
3/2 dy/dx +3=1+dy/dx
1/2 dy/dx =-2
dy/dx =-4 answer
Arthur