How do you find the derivative of #x^3 + (x^2)(y) + y^3 = 9# at P(-1,2)?
1 Answer
Sep 25, 2017
Explanation:
#color(blue)"differentiate implicitly with respect to x"#
#"differentiate "x^2y" using the "color(blue)"product rule"#
#rArr3x^2+x^2dy/dx+2xy+3y^2dy/dx=0#
#rArrdy/dx(x^2+3y^2)=-(3x^2+2xy)#
#rArrdy/dx=-(3x^2+2xy)/(x^2+3y^2)#
#"At "P(-1,2)#
#dy/dx=-(3-4)/(1+12)=1/13#
