Chapter 4.4, Exercise 17

In Exercises 17-29, compute the differential dy.

\(y = x^{2} + 3x - 5\)

\(f'(x^{2} + 3x - 5)\)

\(f'(x^{2} + 3x - 5) = f'(x^{2}) + f'(3x) - f'(5)\)

\(f'(x^{2} + 3x - 5) = 2x^{2-1} + 3f'(x) - 0\)

\(f'(x^{2} + 3x - 5) = 2x + 3\times(1)\)

\(f'(x^{2} + 3x - 5) = 2x + 3\)

\(dy = f'(x^{2} + 3x - 5)dx\)

\(dy = (2x + 3)dx\)