Derivatives of Polynomials

\frac{d}{d x} (5 x^{9} + 6 x^{8} + x^{7} - 7 x^{6} - 10 x^{5} + x^{4} + 2 x^{3} - 4 x^{2} + 8 x + 4)

=

\frac{d}{d x} (5 x^{9}) + \frac{d}{d x} (6 x^{8}) + \frac{d}{d x} (x^{7}) + \frac{d}{d x} (-7 x^{6}) + \frac{d}{d x} (-10 x^{5}) + \frac{d}{d x} (x^{4}) + \frac{d}{d x} (2 x^{3}) + \frac{d}{d x} (-4 x^{2}) + \frac{d}{d x} (8 x) + \frac{d}{d x} (4)

=

5 \frac{d}{d x} (x^{9}) + 6 \frac{d}{d x} (x^{8}) + \frac{d}{d x} (x^{7}) - 7 \frac{d}{d x} (x^{6}) - 10 \frac{d}{d x} (x^{5}) + \frac{d}{d x} (x^{4}) + 2 \frac{d}{d x} (x^{3}) - 4 \frac{d}{d x} (x^{2}) + 8 \frac{d}{d x} (x) + 4 \frac{d}{d x} (1)

=

5 (9 x^{8}) + 6 (8 x^{7}) + (7 x^{6}) - 7 (6 x^{5}) - 10 (5 x^{4}) + (4 x^{3}) + 2 (3 x^{2}) - 4 (2 x) + 8 (1) + 4 (0)

=

45 x^{8} + 48 x^{7} + 7 x^{6} - 42 x^{5} - 50 x^{4} + 4 x^{3} + 6 x^{2} - 8 x + 8

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Copyright © Dayal D. Purohit, Ph.D.(Mathematics)