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(X ^ 4) + (6x ^ (10 / 3)) + 8 * (sqrt (x)) + (12 / x ^ 3.) Find the derivative using the constant multiple rule?

Does anyone may shed some light on this for me?

First, to make things easier, rewrite as: x ^ 4 + 6x ^ (03/10) + 8x ^ (1 / 2) + 12x ^ -3 now take the derivative, it will split into individual pieces and each piece, use the following formula: nx ^ y is derived from (y) nx ^ (y-1) Rather, they multiply by the constant power to find the new constant, and then lower the power by 1. x ^ 4 becomes 4 * x ^ 4-1 = 4x ^ 3 6x ^ (10.03) becomes in (10 / 3) * 6 x ^ (10 / 3 – 3 / 3) = 20x ^ (3.7) 8x ^ (2.1) becomes (1 / 2) * 8 x ^ (1 / 2 – 2 / 2 ) = 4x ^ (-1 / 2) 12x ^ -3 becomes in -3 * 12 x ^ (-3 to 1) =- 36x ^ -4 Therefore, bring these back together (do not forget the + and – signs!) and will need: 4 x ^ 3 + 20x ^ (3.7) + 4x ^ (-1 / 2) – 36x ^ (-4) or rewritten as you had the original: 4 x ^ 3 + 20X ^ (3.7) + 4/sqrt (x) – 36 / x ^ 4

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