SOLUTION: Find an equation of the tangent line to the following graph at the given point cos(x+3y)+sin(y^2)= 1/root( 2) p=((pi/4, 0))

Algebra ->  Linear-equations -> SOLUTION: Find an equation of the tangent line to the following graph at the given point cos(x+3y)+sin(y^2)= 1/root( 2) p=((pi/4, 0))      Log On


   

Question 1034653: Find an equation of the tangent line to the following graph at the given point
cos(x+3y)+sin(y^2)= 1/root( 2)
p=((pi/4, 0))
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Using implicit differentiation, the derivative of
cos%28x%2B3y%29%2Bsin%28y%5E2%29=+1%2Fsqrt%28+2%29 is
-sin%28x%2B3y%29%2A%281%2B3%2A%28dy%2Fdx%29%29%2B2y%2A%28dy%2Fdx%29%2Acosy%5E2+=+0.
==> , after substituting the coordinates of the pint (pi%2F4,0) into the last equation.
==> 1 + 3y' = 0, or y' = -1/3 at x+=+pi%2F4.
==> the tangent at the point (pi%2F4,0) is
y-0+=+%28-1%2F3%29%28x+-+pi%2F4%29, 0r
y+=+-x%2F3+%2B+pi%2F12.