Derivative of Logarithm with trig

[TommG]

Need to find derivative

y = θ(sin(ln θ)) + cos(ln θ)


My work

θ(cos(ln θ))(1/θ) + sin(ln θ) + (-sin(ln θ)(1/θ))

(θcos(ln θ))/θ] + sin(ln θ) + ( (- sin(ln θ))/θ)

cos(ln θ) + [θsin(ln θ) - sin(ln θ)]/ θ

answer in book is 2cos(lnθ)

 

[Ray Vickson]

Need to find derivative

y = θ(sin(ln θ)) + cos(ln θ)


My work

θ(cos(ln θ))(1/θ) + sin(ln θ) + (-sin(ln θ)(1/θ))

(θcos(ln θ))/θ] + sin(ln θ) + ( (- sin(ln θ))/θ)

cos(ln θ) + [θsin(ln θ) - sin(ln θ)]/ θ

answer in book is 2cos(lnθ)

Your answer is correct, and the book's answer is wrong. Are you sure you copied the problem correctly?

 

[TommG]

Your answer is correct, and the book's answer is wrong. Are you sure you copied the problem correctly?

Yeah it is correct

 

[Quesadilla]

I propose that it was supposed to be
\begin{equation*}
y(\theta) = \theta(\sin(\ln \theta) + \cos(\ln \theta)).
\end{equation*}

 

[Ray Vickson]

Yeah it is correct

As Quesadilla points out, the function $f(\theta) = \theta ( \sin(\ln \theta) + \cos(\ln \theta))$ is probably what you want; its derivative agrees with the book's answer.