The weight W of a certain stock of fish is given by W = nw, where n is the size of stock and w is the average weight of a fish. If n and w change with time t as $n = 2 t^2+3$ and $w = t^2-t+2$, then the rate of change of W with respect to t at t = 1, is 

13

We have,

$W=n w, n=2 t^2+3$ and $w=t^2-t+2$

∴  $\frac{d W}{d t}=\frac{d n}{d t} w+n \frac{d w}{d t}, \frac{d n}{d t}=4 t, \frac{d W}{d t}=2 t-1$

At t = 1, we get

$n=5, w=2, \frac{d n}{d t}=4, \frac{d w}{d t}=1$

Hence, $\left(\frac{d W}{d t}\right)_{t=1}=4 \times 2+5 \times 1=13$