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Calculus

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I need to find the derivative of the following problem via logarithmic differentiation, but I'm getting stuck. I know how to solve via logarithmic differentiation, but I can't figure out how to re-write the exponent(s) as logs. Could someone help me?

y= (2x +1)^5(x^4 - 3)^6

  • Calculus - ,

    Well, why do them that way?
    but
    ln y = 5 ln (2x+1) + 6 ln (x^4-3)
    (1/y)dy/dx = 5 (2/(2x+1)) + 6 (4 x^3/(x^4-3))
    now multiply both sides by y which is still (2x +1)^5(x^4 - 3)^6

    ps - I would have just done it as a product of functions of x

  • Calculus - ,

    log y = 5 log (2x+1) + 6 log (x^4 -3)
    (1/y)*dy/dx = 10/(2x +1) + 24 x^3/(x^4 -3)
    dy/dx = (2x +1)^5(x^4 - 3)^6 *
    [10/(2x +1) + 24 x^3/(x^4 -3)]

    Check my work

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