# What is the slope of #xy^3+xy=10# at the point #(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"#