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Math Help - Derivatives: Logarithmic Differentiation

  1. #1
    Junior Member
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    Derivatives: Logarithmic Differentiation

    So i solved a few of the steps but i'm stuck at this one step and can't move on

    Find y if

    y=(10x+9)^10x+1


    Note: The product of two numbers or two expressions should be entered as a*b. For the quotient of two numbers use a/b. For the power use a^b.

    1. Take the natural logarithm of both sides:
    lny = ln (10*x+9)^(10*x+1)

    2. Simplify by using properties of logarithms:
    Important! In your answer, lna must be entered as log(a).
    lny = (10*x+1)*log(10*x+9)

    3. Differentiate both sides with respect to x:
    yy = (Help please)

    4. Solve for y:
    y = y( )

    5. Substitute the original expression for y to get y in terms of x only:
    y =


    If someone could help me from 3 onwards i would really appreciate it.

    Thanks
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  2. #2
    Senior Member BAdhi's Avatar
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    Gampaha, Sri Lanka
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    Thanks
    6
    can't you use \frac{d(uv)}{dx}=\frac{du}{dx}.v+\frac{dv}{dx}.u

    then y'y =(10x+1) \frac{10}{(10x+9)} + 10ln(10x+9)
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  3. #3
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    Ah that was it, thanks a lot!
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