Sample question
given that $\frac{dW}{dt}=\frac{1}{25}(W-300)$
what is the $\frac{dW^2}{d^2t}$?
Textbook answer
The textbook said that we can multiple $\frac{1}{25}$ to the first derivative to find the second derivative but I thought that the answer was just to take the derivative of the first derivative.
How can the textbook be right?
$$ \dfrac{d^2W}{dt^2} = \dfrac{d}{dt}\left(\dfrac{dW}{dt}\right) = \dfrac{d}{dt}\left(\dfrac{1}{25}(W-300)\right) = \dfrac{1}{25}\dfrac{dW}{dt} - \dfrac{1}{25}\dfrac{d 300}{dt} = \dfrac{1}{25}\left(\dfrac{1}{25}(W-300)\right).$$