Derivatives of Polynomials

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

=

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

=

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

=

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

=

32 x^{7} - 42 x^{6} - 20 x^{4} - 28 x^{3} + 18 x^{2} - 8

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