Dividend: x3+4x2-9x-36 Divisor: x+3 Quotient: x2+x-12
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.
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 - 3x - 6) / 6 = (3x + 2) / 2 ∴2(3x + 2) = 6(3x + 2) ∴6x + 4 = 18x = 12 ∴12x = -8 ∴x = -2/3
You have to specify more information than that. If y is an independent variable and you're talking about the derivative with respect to x, it would be 1/y.
1 divided by x to the third power equals x to the negative third. The derivative of x to the negative third is minus three x to the negative fourth.
2
x-8
x - 3
x - 5
x
7x + 8
Following the correct order of operations: derivative of x^2 + 6/2 = derivative of x^2 +3, which equals 2x
x = 0,1
The answer to x4+x3-14x2+4x+6 divided by x-3 is x3+4x2-2x-2
4
Why would you ask that? Stuck on your maths homework? x=1/2