# 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