Friday

August 29, 2014

August 29, 2014

Posted by **marcus** on Monday, December 8, 2008 at 4:02am.

- calculus -
**drwls**, Monday, December 8, 2008 at 6:19amUse implicit differentiation.

Differentiate both sides of the equation with respect to x, treating y as a function of x.

x cosy dy/dx + sin y - 2 sin 2y dy/dx = -sin y dy/dx

Now solve for dy/dx. It will be a function of both x and y.

You could also differentiate both sides with respect to y, solve for dx/dy, and take the reciprocal of the answer. The result will look different but will still be correct.

x cos y + sin y dx/dy - 2 sin 2y = -sin y

dx/dy = [-siny + 2 sin2y -x cos y]/sin y

dy/dx = sin y/[-siny + 2 sin2y -x cos y]

**Related Questions**

AP Calculus - Determine dy/dx if xsiny=artany i did (x)(cosy dy/dx) so far

AP Calculus - I previously posted this but had a mistake in it. Determine dy/dx...

Calculus...plz help!! - find dy/dx of xsiny-ycosx=1

integral Calculus - ʃsin y dy/ √1 + cosy please help..thanks.. that's...

Ap Calc AB - Find the equation of the line normal to the curve at (0,0). (Normal...

Calculus - find y' if sin^-1(xy)=cosy

Pre-calculus - If cosx=4/5, cosy=12/13 in Quad. IV, find sin(x+y)

Pre-calculus - If cosx=4/5, cosy=12/13 in Quad. IV, find sin(x+y)

Trigo help! - Ok, i've tried this question, and it brings me to no answers. ...

Trigonometry Help - Simplify: sin(x-y)cosy+cos(x-y)siny = (sinxcosy-cosxsiny)...