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A little background, though not necessarily needed:

A ladder of length 5m has been put in the first quadrant of the coordinate system, resting on the axes.

$$x^2+y^2=5^2$$

The angle between the x-axis and the ladder: $\cos{\theta} = \frac{x}{5}$. I should implicitly differentiate to find $\theta'(x)$, but I don't know how to proceed. The $\theta$ is inside a cosine function. This is new.

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This is just the chain rule. The derivative of $\cos\theta$ with respect to $x$ (where $\theta$ is a function of $x$) is $\theta'\cdot (-\sin\theta)$

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  • $\begingroup$ That's depressingly simple and I feel ashamed. Oh my. But thank you for the answer! $\endgroup$
    – Felix
    Commented Nov 16, 2017 at 14:06
  • $\begingroup$ @Felix No reason to feel ashamed. Some times all the trees do hinder us from seing the forest, and it happens to all of us. $\endgroup$
    – Arthur
    Commented Nov 16, 2017 at 14:07

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