# How do you use implicit differentiation to find the slope of the curve given #x^2y=x+2# at (2,1)?

##### 2 Answers

#### Explanation:

differentiate

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

#color(blue)"product rule"# is required to differentiate#x^2y#

#x^2.dy/dx+2xy=1#

#rArrdy/dx=(1-2xy)/x^2# Use the point (2 ,1) to evaluate

#dy/dx# which gives the slope.

#dy/dx=(1-(2xx2xx1))/2^2=-3/4#

Please see the explanation for the procedure. The slope is

#### Explanation:

I will explain each term.

Term 1:

Term 2:

Term 3:

Put these back into their corresponding locations in the equation:

Solve for

The slope, m, is the above evaluated at the point