What is the slope of xy^3+xy=10xy3+xy=10 at the point (5,1)(5,1)?
2 Answers
Jul 13, 2017
Slope
Explanation:
Applying implicit differentiation:
Slope of the tangent
Mar 30, 2018
Explanation:
"differentiate "color(blue)"implicitly with respect to x"
"differentiate "xy^3" and "xy" using the "color(blue)"product rule"
#(x.3y^2dy/dx+y^3 .1)+(xdy/dx+y.1)=0#
rArr3xy^2dy/dx+y^3+xdy/dx+y=0
rArrdy/dx(3xy^2+x)=-y^3-y
rArrdy/dx=-(y^3+y)/(3xy^2+x)
"at "(5,1)
dy/dx=-(1+1)/(15+5)=-2/20=-1/10larrcolor(red)"slope"