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Math Help - Differentiation? Equation of the tangent line?

  1. #1
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    Differentiation? Equation of the tangent line?

    I'm new to Calculus and am having a hard time adjusting to the new environment of University! Thanks all for looking.

    f(x) = 4pi^4

    f'(x) = ?

    --------------------------------------------------

    Find an equation of the tangent line to the curve at the given point.
    (Assume the tangent line form to be f(x) = mx + b.)

    y=e^x/x (1, e)

    m= ?
    b= ?

    ----------------------------------------------------

    Find f '(x) and f ''(x). f(x) = x^9e^x

    f'(x) = ?
    f''(x) = ?


    Thanks again. These are the problems I left for last and I have no idea how to solve them.
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  2. #2
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    Quote Originally Posted by akifbayram View Post
    I'm new to Calculus and am having a hard time adjusting to the new environment of University! Thanks all for looking.

    f(x) = 4pi^4

    f'(x) = ?

    what is the derivative of a constant?

    --------------------------------------------------

    Find an equation of the tangent line to the curve at the given point.
    (Assume the tangent line form to be f(x) = mx + b.)

    y=e^x/x (1, e)

    find y'(x) and evaluate y'(1) to get the slope of the tangent line.

    ----------------------------------------------------

    Find f '(x) and f ''(x). f(x) = x^9e^x

    use the product rule to find f'(x) ... you'll have to use it again to find f''(x)

    f'(x) = ?
    f''(x) = ?
    ...
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  3. #3
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    1. 0 ?

    2. Working on that...

    3. f'(x) = (9x^8)(e^x) + (x^9)(xe^(x-1))
    = e^(x-1) x^8 (x^2+9 e)

    f''(x)= Working on this too..
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  4. #4
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    Quote Originally Posted by akifbayram View Post
    1. 0 ? yes

    2. Working on that...

    3. f'(x) = (9x^8)(e^x) + (x^9)(xe^(x-1)) no ... what is the derivative of e^x?
    ...
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  5. #5
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    Derivative of e^x is itself?

    so it would be...
    f'(x)=(9x^8)(e^x)+(x^9)(e^x))
    f'(x)=(e^x) (x^8) (x+9)
    f''(x)=e^x(8x^7)+e^x(x^8)*(x+9)+(e^x)(x^8)(1)
    f''(x)=(e^x)(x^9+10)(e^x)(x^8+8)(e^x)(x^7)
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  6. #6
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    f(x) = x^9 e^x

    f'(x) = x^9 e^x + 9x^8 e^x

    f'(x) = e^x(x^9 + 9x^8)

    f''(x) = e^x(9x^8 + 72x^7) + e^x(x^9 + 9x^8)

    f''(x) = e^x[(9x^8 + 72x^7) + (x^9 + 9x^8)]

    f''(x) = e^x(x^9 + 18x^8 + 72x^7)

    f''(x) = x^7 e^x(x^2 + 18x + 72)
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