Implicit Differentiation | University of Cambridge - Edubirdie

University:
University of Cambridge
Course:
0580 IGCSE | Mathematics
Academic year:

2024
Views:

444

Pages:

2
Author:

Shahbaz A.

implicit differentiation shahbaz ahmed July 2024 Ex 3.7 THOMAS calculus Twelfth Edition Q4 x3 − xy + y 3 = 1 d(x3 −xy+y 3 ) dx d(x3 ) dx − d dx (1) = d(xy) dx + d(y 3 ) dx dy 3x2 − [x dx + y dx dx ] + =0 d(y 3 ) dy dy dx =0 dy dy 3x2 − x dx − y + 3y 2 dx =0 dy dy −x dx + 3y 2 dx = −3x2 + y dy (−x + 3y 2 ) dx = −3x2 + y dy −(x − 3y 2 ) dx = −(3x2 − y) dy (x − 3y 2 ) dx = (3x2 − y) dy dx = 3x2 −y x−3y 2 Q7 y2 = x−1 x+1 y 2 (x + 1) = x − 1 d[y 2 (x+1)] dx = dx dx − d dx (1) 2 ) y 2 d[(x+1)] + (x + 1) d(y dx dx = 1 y 2 [ dx dx + d dx (1)] 2 ) dy + (x + 1) d(y dy dx = 1 1 dy y 2 [1 + 0] + (x + 1)(2y) dx =1 dy y 2 + 2y(x + 1) dx =1 dy = 1 − y2 2y(x + 1) dx dy 2y(x + 1) dx = 1 − y2 dy dx = 1−y 2 2y(x+1) 2

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