TheIntegral From: US Posts: 26 Votes: 104 |
Find the derivative of the function f(x)= 1/7 x^7+(x^2+6)(x^2-x-6)+27 a. f’(x)=7x3-15x-2 b. f’(x)=x3+3x2+4 c. f’(x)=4x6+7 d. f’(x)=x6+4x3-3x2-6 |

MythGenius90 From: US Posts: 42 Votes: 84 |
You will need to know these formulas: (d/dx)(x^n) = nx^(n-1) (d/dx)(f(x) + g(x)) = f'(x) + g'(x) (d/dx)(f(x) - g(x)) = f'(x) - g'(x) (d/dx)(f(x)g(x)) = f'(x)g(x) + f(x)g'(x) f'(x) = (1/7)(7)x^6 + 2x(x^2 - x - 6) + (x^2 + 6)(2x - 1) = x^6 + 2x^3 - 2x^2 - 12x + 2x^3 - x^2 + 12x - 6 = x^6 + 4x^3 - 3x^2 - 6 which is d PLEASE RATE LIFESAVER if this helps you. THANKS. |

Anonymous From: - Posts: - Votes: - |
Well let's simplify the equation first and go from there. Thanks a funky looking equation so well try and get rid of the parts in parenthesis. f(x) = (1/7)x^7 + (x^4-x^3-6x^2+6x^2-6x-36) + 27 Now -6x^2 and + 6x^2 cancel and -36 can be combine with 27 so we are left with.... f(x) = (1/7)x^7 + x^4 - x^3 - 6x -9 That's much easier to derive. So the answer unsimplified will look like... f'(x) = 7*(1/7)x^6 + 4x^3 - 3x^2 - 6 - 0 So pick the answer choice closest to that. Remember, before you try to derive or integrate you can always do things like simplify the expression or even break it up into smaller more manageable parts. |

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