관련 변화율

Since $A=0$, the equation relating the variables tells us:

$$\begin{aligned} 0&=\log\left(C^2+D^2+1\right)\\ 1&=C^2+D^2+1\\ 0&=C^2+D^2\\ 0&=C=D \\ \text{This will probably be useful information. Since we're also given the value of a derivative, let's differentiate the equation relating the variables implicitly with respect to $t$. For ease of notation, we will write $\displaystyle \frac{\mathrm{d}A}{\mathrm{d}t}=A'$, etc.} \\ A'B+AB'&=\frac{2CC'+2DD'}{C^2+D^2+1} \\ \text{At $t=10$, $A=C=D=0$:} \\ A'B+0&=\frac{0+0}{0+0+1}\\ A'B&=0 \\ \text{at $t=10$, $A'=2$ units per second:} \\ 2B&=0\\ B&=0. \end{aligned}$$