Derivatives of Polynomials

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

=

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

=

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

=

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

=

90 x^{8} + 40 x^{7} - 35 x^{6} - 12 x^{5} + 40 x^{4} + 16 x^{3} + 9 x^{2} + 16 x - 7

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