sin Diff Problem

[Jason76]

\(\displaystyle f(x) = \sin(3 \ln x)\)

\(\displaystyle f'(x) = \cos(u) du\)

\(\displaystyle f'(x) = \cos(u) \dfrac{3}{x}\)

\(\displaystyle f'(x) = \cos(3 \ln x) \dfrac{3}{x}\)

 

[Deleted member 4993]

\(\displaystyle f(x) = \sin(3 \ln x)\)

\(\displaystyle f'(x) = \cos(u) du\)

\(\displaystyle f'(x) = \cos(u) \dfrac{3}{x}\)

\(\displaystyle f'(x) = \cos(3 \ln x) \dfrac{3}{x}\)

Where is the confusion??!

 

[daon2]

\(\displaystyle f(x) = \sin(3 \ln x)\)

\(\displaystyle f'(x) = \cos(u) du\)

That is not correct.

\(\displaystyle f'(x) = \cos(u) \dfrac{3}{x}\)

\(\displaystyle f'(x) = \cos(3 \ln x) \dfrac{3}{x}\)

Your final answer is correct.

 

[HallsofIvy]

\(\displaystyle f(x) = \sin(3 \ln x)\)

\(\displaystyle f'(x) = \cos(u) du\)

You should have "du/dx" not just "du". And you should state "u= 3 ln(x)" before writing this.

\(\displaystyle f'(x) = \cos(u) \dfrac{3}{x}\)

\(\displaystyle f'(x) = \cos(3 \ln x) \dfrac{3}{x}\)

Yes, this is correct.