Implicit Differentiation: ln(xy) = cos(x)

[johnboy]

Find the derivative

ln(xy) = cos(x)
1/(xy) (y+x dy/dx) = -sin(x)
y+x dy/dx = xy (-sin(x))
x dy/dx = xy(-sin(x)) -y
dy/dx = (xy(-sin(x)-y)/x

Did i do it correctly? Thank you.

 

[pka]

Yes you did.
Here is a note: it is easier to read \(\displaystyle y'\) rather than \(\displaystyle \frac{dx}{dy}\).

 

[stapel]

Here is a note: it is easier to read \(\displaystyle y'\) rather than \(\displaystyle \frac{dx}{dy}\).

Easier for some. But I find that I tend to "lose" the appostrophe on the "y'", so I use "dy/dx" so as to better keep track of my work.

Naturally, "diff'rent strokes for diff'rent folks".

Eliz.

 

[johnboy]

I'm the same way, Eliz.

 

[pka]

Well, I actually agree with Eliz as long as the poster uses LaTeX.
But trying to read an ordinary typing of (dx/dy) in a complicated expression is much more difficult than reading y’. My point was about the appearance and not about the way one chooses to do the problem. I would suggest learning top use LaTeX.