Find y′ if cosxy = 4x^2 +1?

2 ⤊

2006-12-18 08:35:45 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics

Just differentiate both sides and solve for y':

-(y + xy')sin(xy) = 8x

So y' = -(8x + ysin(xy))/(xsin(xy)).

2006-12-18 08:40:16 · answer #1 · answered by acafrao341 5 · 1⤊ 0⤋

Differentiating implicitly:
(cosxy = 4x^2 +1)'
-sin(xy)*(xy'+y)=8x
(xy'+y)=-8x/sin(xy)
xy'=-8x/sin(xy) - y
y'=(-8x/sin(xy)-y)/x

2006-12-18 16:39:11 · answer #2 · answered by maegical 4 · 1⤊ 0⤋