Help with differential understanding

[Bestfrog]

Homework Statement

A simple pendulum in quiet is released from the horizontal ($\theta=0$) ($\theta=90$ for the vertical). Will the pendulum cover in the smaller time the arch from $\theta=0$ to $\theta=30$ or from $\theta=30$ to $\theta=90$?

The Attempt at a Solution

I would like to know one thing: by the conservation on law, the speed in function of $\theta$ is $v=\sqrt{2glsin\theta}$. Then I found a solution that says: "taking the differential I get $dv= \sqrt{2gl} \frac{cos\theta}{2 \sqrt{sin\theta}} d\theta$. How can this passage is possible? I don't understand what happen

 

[MarkFL]

Suppose you are given:

$f(u)=k\left(\sin(u)\right)^{\frac{1}{2}}$

Using the power and chain rules, what do you get for:

$\dfrac{df}{du}=?$

 

[cnh1995]

taking the differential I get dv=√2glcosθ2√sinθdθdv=2glcosθ2sinθdθdv= \sqrt{2gl} \frac{cos\theta}{2 \sqrt{sin\theta}} d\theta. How can this passage is possible? I don't understand what happen

It is based on the chain rule of differentiation. Have you studied differentiation?

 

[Bestfrog]

Yes I know. Now I understand the physical meaning