find the derivative of this function f(x) = (x2 - x + 1) (x3 - 2 )?

Question

please help with step by step detailed instruction. not looking for just the solution but the entire process because i simply don't understand.

Answer 1

the derivative of a multiplication follows this rule: derivative of first term times the second term plus derivative of second term times the first term. so:
(2x-1)(x^3-2)+(3x^2)(x^2-x+1)

Answer 2

Rule 5) to locate the by-product of the made from 2 purposes, take the first cases the by-product of the 2d and upload it to the 2d cases the by-product of the first. p(x) = (x^3 + 2x + 4)(2x^2 + x + 5) by-product of p(x) = (x^3 + 2x + 4)(4x + a million) + (2x^2 + x + 5)(3x^2 + 2) amplify 4x^4 + 8x^2 +16x + x^3 + 2x + 4 + 6x^4 + 3x^3 + 15x^2 + 4x^2 + 2x + 10 then integrate/simplify words 4x^4 + 6x^4 + x^3 + 3x^3 + 8x^2 + 15x^2 + 4x^2 + 16x + 2x + 2x + 4 + 10 10x^4 + 4x^3 + 27x^2 + 20x + 14

Answer 3

These are best done (in my opinion) by multiplying them all out and differentiating term by term. I can do this easily in my head....you will too eventually.

(x^2 - x + 1) (x^3 - 2 )

==> x^5 - 2x^2 - x^3 + 2x + x^3 - 2
==> x^5 - 2x^2 + 2x - 2 [combine the 'like' terms]

So, you have:

f(x) = x^5 - 2x^2 + 2x - 2

Now take the derivative....term-by-term.

df/dx = 5x^4 - 4x + 2

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That's all there is to it. Did you follow?

Answer 4

x^2 - x + 1) (x^3 - 2 )

x^5 - 2x^2 - x^3 + 2x + x^3 - 2
x^5 - 2x^2 + 2x - 2



f(x) = x^5 - 2x^2 + 2x - 2



df/dx = 5x^4 - 4x + 2

Answer 5

f´(x) =( 2x-1)*(x^3-2) + (x^2-x+1)* (3x^2)

Answer 6

dy=udv+vdu
=(2x-1)(x3-2)+(3x2)(x2-x+1)