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What is the answer to x cubed plus 4x squared minus 9x minus 36 divided by x plus 3?
Dividend: x3+4x2-9x-36 Divisor: x+3 Quotient: x2+x-12
How do you differentiate y equal to one third x cubed minus 3x squared plus 8x plus one third?
The derivative of y = 1/3 x3 - 3x2 + 8x + 1/3 is x2 - 6x + 8. You can determine this for yourself by the rules. The derivative of a constant (e.g. 1/3) is 0. The derivative of xn for positive n (actually all nonzero n) is nxn-1. And if the derivative of f(x) is f'(x), then the derivative of k f(x) is k f'(x). Put all these together and you get the above result.
What is the answer to the problem X cubed plus six x squared plus three x plus one divided by x minus two?
Your answer will depend on the parameters of the instructions. If you're looking for the first derivative, simply use the product rule by changing the denominator to a negative exponent and bringing it up (take the negative square root of the quantity x-2 to the top). Then, follow the rules of calculus and algebra. Wow, that's a mess. Let's see... you get "the quantity x cubed plus 6x squared plus 3x plus 1 times the quantity -1(x-2) raised to the negative second plus the quantity x-2 raised to the negative first times the quantity 3x squared plus 12x plus 3." This is because of the Product Rule. Simplifying (by factoring out (x-2) raised to the negative second and combining like terms) gives us "(x-2) raised to the negative second times the quantity 2x cubed minus 24x minus 7." This can also be written as "2x cubed minus 24x minus 7 all over the quantity x-2 squared." f'(x)= 2x^3-24x-7 (x-2)^2
X minus 3X minus 6 divided 6 equals 3X plus 2 divided by 3?
(x - 3x - 6) / 6 = (3x + 2) / 2 ∴2(3x + 2) = 6(3x + 2) ∴6x + 4 = 18x = 12 ∴12x = -8 ∴x = -2/3
What is the derivative of 3X squared plus 5x plus 2?
f(x) = 3x2 + 5x + 2fprime(x) = 6x + 5
