Determining the derivative of a natural logarithmic funtion

[Elisabeth V kessel]

Heey everyone, I have been staring at this natural logarithm function for over an hour now and still do not understand how I can derive the derivative. The answer is given but I do not see how exactly they come to 3.ln (x^2 =4.x)/2

Could someone please try to explain how this works as I did watch a few youtube vids on logr funtion derivatives. (I used the product rule in order to determine the derivative)

I would be very thankfull if someone could explain which steps I have to take in order to get here.

 

[skeeter]

are you familiar with the properties of logarithms?

[math]f(x) = \ln[(x^2+4x) \cdot \sqrt{x^2+4x}][/math]
[MATH]f(x) = \ln(x^2+4x)^{3/2}[/MATH]
[MATH]f(x) = \dfrac{3}{2} \ln(x^2+4x)[/MATH]
[MATH]f’(x) = \dfrac{3}{2} \cdot \dfrac{2x+4}{x^2+4}[/MATH]
[MATH]f’(x) = \dfrac{3(x+2)}{x(x+4)}[/MATH]
can you find f’(2) ?

 

[JeffM]

Please do not double post

 

[Elisabeth V kessel]

thank you so much!!! I understand and see it now