I need help on the process of solving this derivative. How do I go about solving this derivative. f(x)=ln((7x)/(x+4))

ridge041h

ridge041h

Answered question

2022-09-06

I need help on the process of solving this derivative.
How do I go about solving this derivative.
f ( x ) = ln ( 7 x x + 4 )
I go from this to
1. f ( x ) = ln ( 7 ) + ln ( x ) ln ( x + 4 )
and then
2. f ( x ) = 1 x 1 x + 4
then
3. f ( x ) = x + 4 x x ( x + 4 )
and end up with
4. f ( x ) = 4 x ( x + 4 )
which is the correct answer. This procedure is what we did in class, but I do not get how I went from step 2 to 3 which is what has me confused. A step by step explanation would be greatly appreciated. Thanks!

Answer & Explanation

Gabriela Werner

Gabriela Werner

Beginner2022-09-07Added 11 answers

That was simply finding the common denominator, which is x ( x + 4 )
x divides x ( x + 4 ) to give us 1 ( x + 4 ) in the numerator, and x + 4 divides x ( x + 4 ) to give us 1 x which we subtract from the first term in the numerator. Then simplify ( x + 4 ) x = 4 in the numerator.
ubwicanyil5

ubwicanyil5

Beginner2022-09-08Added 2 answers

Using the chain rule:
f ( x ) = ( x + 4 7 x ) ( 7 x x + 4 ) = ( x + 4 7 x ) ( 28 ( x + 4 ) 2 ) = 4 x ( x + 4 )

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