derivative of log base 4 (x^2)?

I tried converting it to ln x^2 divided by ln 4 (idk if I used change of base correctly), and trying to find the derivative by using the quotient rule and the fact that d/dx of ln x is = to 1/x.  Alas, I didn't get the same answer... I got  (2)/(x ln 4), but that wasn't it... could someone walk me through it, showing out every step!! Thank you!!

Also point out to me what properties of derivatives and logs you are using, and anything else that may be helpful. Thanks!! 

2 Answers

  • 1 month ago
    Favorite Answer

    log(base a) x = [ log(base b) x ] / [ log(base b) a ]

    log₄x² = ln x² / ln 4 = 2 ln x / ln 4

    y = (2/ln 4)(ln x)

    y' = (2/ln 4)(1/x)

    you are correct.

  • Vaman
    Lv 7
    1 month ago

    ln x= y, x=e^y, 1= e^y dy/dx, dy/dx= 1/e^y= 1/x

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