Mathematics, 15.01.2020 05:31 zitterkoph
Differentiating a logarithmic function in exercise, find the derivative of the function. see examples 1, 2, 3, and 4.
y = ln[x(2x + 3)2]
Answers: 1
![y=\ln[x(2x+3)^2]](/tpl/images/0455/6461/2c4d4.png)
![\dfrac{dy}{dx}=\dfrac{1}{[x(2x+3)^2]}\times [x'(2x+3)^2+(2x+3)^2'x]\\\\\dfrac{dy}{dx}=\dfrac{1}{[x(2x+3)^2]}\times [(2x+3)^2+2x(2x+3)]\\\\\dfrac{dy}{dx}=\dfrac{4x^2+9+12x+4x^2+6x}{x(2x+3)^2}\\\\\dfrac{dy}{dx}=\dfrac{8x^2+18x+9}{x(2x+3)^2}](/tpl/images/0455/6461/e5ff0.png)
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Differentiating a logarithmic function in exercise, find the derivative of the function. see example...
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