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