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SOLUTION :
a.
d/dx (7x^3 + 5x^2 - 10x + 3)
= 7 * 3 x^(3 - 1) + 5 * 2 x^(2 - 1) - 10 * 1 * x^(1 - 1) + 0
= 21 x^2 + 10x - 10 (ANSWER).
b.
d/dx (x^3 arctan(x))
= d/dx(x^3) arctan(x) + x^3 d/dx (arctan(x))
= 3 x^2 arctan(x) + x^3 * 1/(1 + x^2)
= 3x^2 arctan(x) + x^3 / (1 + x^2) (ANSWER).
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