MAT 1300 Lecture 11: MAT 1300 LECTURE 11- IMPLICIT DIFFERENTIATION

• School: University of Ottawa
• Department: Mathematics
• Course: MAT 1300
• Professor: Hung-Chang Liao

Document Summary

Consider the circle given by the equation x^2 +y^2 = 25. One method is to solve y in terms of x y^2 = 25-x^2 y = +or - (sqrt (25- x^2) (3,4) is on the upper half so take y = (sqrt (25- x^2) Review of chain rule u= g(y) and y =f(x) Example : if x^2 +y^2 = 25 find dy/dx at the point (3,4) Step 1 : differentiate both sides with respect to x d/dx(x^2 +y^2 )=d/dx( 25) 2y . dy/dx = -2x dy/dx= -2x/2y dy/dx = -x/y. To find dy/dx from from an equation involving x and y differentiate both sides with respect to x solve for dy/dx. Find dy/dx in terms of x and y. Find the equation of the tangent line at the given point. X^2 -3xy+7y =5 at point (2,1) d/dx(x^2 -3xy+7y )= d/dx(5) 2x-3y -3x. dy/dx + 7. dy/dx =0 (7-3x) . dy/dx = 3y -2x dy/dx = 3y -2x/ (7-3x)