What is the derivative of $\log \left(\sin ^2 x\right)$ with respect to $\sin x$ ?

Let $S_n$ denote the sum of the first $n$ terms of a sequence $a_1, a_2, a_3, \ldots$. If $S_{n+3}-S_n=13 n+7$ for all $n$, what is the value of $a_{13}-a_{10}$ ?

Five fair coins are tossed independently. What is the probability that at least two heads appear?

Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be the function defined by

$$ f(x)= \begin{cases}x^2-4 x-5 & \text { if } x \geq 1, \\ 2 x & \text { if } x<1 .\end{cases} $$

Which one of the following statements is TRUE?