MATH 140 Lecture Notes - Lecture 12: Quotient Rule, Differentiable Function

• School: University of Maryland
• Department: Mathematics
• Course: MATH 140
• Professor: Gulick

Document Summary

Examples of implicitly defined functions: o o x2+ y2=4 exy+x2 y3= . =0: derive: 2x+2y dy dx, solve for dy/dx: 2y dy dx. = x y: thus, dy dx at ( 1, )= 1, find the equation of the tangent line at the point given above: y = 1 (x+1) =0+3 x2 y3+3 x3 y2 dy dx: derive: 2y dy dx, move dy/dx to one side: 2y dy dx. 2y+2 3 x3 y2=3 x2 y3 dy dx: divide: dy dx. Ex4: for x = 2 and y = 1 in ex3, find the derivative: check coordinates in original equation: ( 1)2+2( 1)=7+23( 1)3 1 2=7 8 1= 1, plug in numbers: Y dy dx y2 d2 y d x2 = ( x) Ex6: find the derivative of x=tan(x2 y3: chain rule: 1=[sec2(x2 y3)][2x y3+3 x2 y2 dy dx o o o o.