# How do you implicitly differentiate #-y= x^3y^2-3x^2y^2-7x^2y^4 #?

##### 1 Answer

Jan 21, 2016

#### Explanation:

This implicit differentiation makes heavy use of the product rule. Before differentiating the function, we should do a sample first:

#d/dx[5x^4y^2]=5y^2d/dx[x^4]+5x^4d/dx[y^2]=5y^2(4x^3)+5x^4(2y)dy/dx#

The most important part about this is that differentiating any term with a

Differentiating the given function:

#-dy/dx=3x^2y^2+2x^3ydy/dx-6xy^2-6x^2ydy/dx-14xy^4-28x^2y^3dy/dx#

Solve for

#28x^2y^3dy/dx+6x^2ydy/dx-2x^3ydy/dx-dy/dx=3x^2y^2-6xy^2-14xy^4#

Factor out a

#dy/dx=(x^2y^2-6xy^2-14xy^4)/(28x^2y^3+6x^2y-2x^3y-1)#