Question

1. y = sin? (In x). Find dy

Show your work. en nuov vlomia
A.
sin (In x2)
х
cos? (In x)
c. sin (In x) cos(Inx)
D.
2 sin (In x) cos(In x)
E. None of the above.

Answer 1

dy/dx= cos(ln(x))/x

Explanation:

y=sin(ln(x)) given

We have to use chain rule to differentiate!

Let u=ln(x) then du/dx=1/x

So we have

if y=sin(ln(x)) then y=sin(u) and dy/dx=dy/du * du/dx=cos(u) *1/x

where again u=ln(x) so

dy/dx=cos(ln(x)) *1/x

dy/dx=cos(ln(x))/x

I hope I have the right intepretation because I do see a ? in between sin and (ln(x)) .