# How do you find #(dy)/(dx)# given #x^2+xy-y^3=7#?

##### 1 Answer

Mar 8, 2018

#### Explanation:

#color(blue)"differentiate implicitly with respect to x"#

#"noting that"#

#•color(white)(x)d/dx(y)=dy/dx#

#•color(white)(x)d/dx(y^2)=2ydy/dx#

#•color(white)(x)d/dx(y^3)=3y^2dy/dx#

#"differentiate "xy" using the "color(blue)"product rule"#

#rArr2x+(xdy/dx+y)-3y^2dy/dx=0#

#rArrdy/dx(x-3y^2)=-y-2x#

#rArrdy/dx=-(y+2x)/(x-3y^2)#