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