DIFFERENTIAL CACULUS with MATLAB by SCIENTIFIC BOOKS

Author:SCIENTIFIC BOOKS
Language: eng
Format: mobi, epub
Published: 2016-01-15T22:00:00+00:00

Exercise 4-10. Calculate the implicit derivative of y with respect to x, where x and y satisfy the following equation:

x3 + 3 x2y3 + 5xy + 6y3 = 8

First, we will use the operator D to differentiate the equation:

» pretty (sym (maple ('D(x^3+3*x^2*y^3+5*x*y+6*y^3=8)')))

2 3 2 2 2

3 D(x) x + 6 D(x) x y + 9 x D(y) y + 5 D(x) y + 5 x D(y) + 18 D(y) y = 0

Now we replace D (x) with 1 and solve for D (y):

» pretty (sym (maple ('subs (D (x) = 1, D(x^3+3*x^2*y^3+5*x*y+6*y^3=8))')))

2 3 2 2 2

3 x + 6 x y + 9 x D(y) y + 5 y + 5 x D(y) + 18 D(y) y = 0

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