# Question #f73f9

##### 1 Answer

Feb 2, 2017

#### Explanation:

#color(orange)"Reminder "m_("tangent")=dy/dx# differentiate

#color(blue)"implicitly with respect to x"# Both terms on the left side require to be differentiated using

the#color(blue)"product rule"#

#(x.3y^2dy/dx+y^3 .1)+(x.dy/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)# Substitute the coordinates of (5 ,1) into

#dy/dx#

#rArrdy/dx=-2/(15+5)=-1/10#