How do you use implicit differentiation to find dy/dx given #y^2=2+xy#?

2 Answers
Feb 15, 2017

#dy/dx= y/(2y-x)#

Explanation:

Differentiate both sides of the equation with repect to #x#:

#d/dx y^2 = d/dx (2+xy)#

#2y dy/dx = y+x dy/dx#

Solve for #dy/dx#:

#dy/dx(2y-x) = y#

#dy/dx= y/(2y-x)#

Feb 15, 2017

#dy/dx=y/(2y-x)#

Explanation:

differentiate each term on both sides #color(blue)"implicitly with respect to x"#

Use the #color(blue)"product rule"# on the term xy

#rArr2ydy/dx=0+(x.dy/dx+y.1)#

#rArrdy/dx(2y-x)=y#

#rArrdy/dx=y/(2y-x)#