Implicit differentation of $\cos y(x) = f(x)$

Question

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.

Answer 1

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