How do you find #dy/dx# by implicit differentiation given #x^2+3xy+y^2=0#?
3 Answers
Given:
Differentiate each term with respect to x:
Use the power rule,
Use the product rule,
Use the chain rule,
The derivative of a constant is 0:
Distribute the 3:
Move all of the terms that do not contain
Factor out
Divide by
Explanation:
#"differentiate "color(blue)"implicitly with respect to x"#
#"the term " 3xy" is differentiated using the "color(blue)"product rule"#
#rArr2x+3(x.dy/dx+y.1)+2y.dy/dx=0#
#rArr2x+3xdy/dx+3y+2ydy/dx=0#
#rArrdy/dx(3x+2y)=-2x-3y#
#rArrdy/dx=-(2x+3y)/(3x+2y)#
Explanation:
From
then