$A$ cube of ice melts without changing its shape at a uniform rate of $4 \, cm^3/min$. The rate of change of the surface area of the cube,in $cm^2/min$,when the volume of the cube is $125 \, cm^3$,is:

Find the rate of change of $\sqrt{x^2 + 16}$ with respect to $\frac{x}{x - 1}$ at $x = 3$.

For the curve $y=5x-2x^3$,if $x$ increases at the rate of $2 \text{ units/sec}$,the rate of change in the slope of the curve at $x=3$ is ......../sec

$A$ particle moves in a straight line such that its displacement $S$ (in $m$) at a time $t$ (in $sec$) is given by $S(t) = t^3 - 4t^2 + 7t$. The instantaneous velocity $v$ at $t = 4$ is (in $m/sec$)

$A$ balloon starting from rest is ascending from the ground with a uniform acceleration of $4 \ ft/sec^2$. At the end of $5 \ sec$, a stone is dropped from it. If $T$ is the time taken for the stone to reach the ground and $H$ is the height of the balloon when the stone reaches the ground, then:

The side of an equilateral triangle is increasing at the rate of $2 \text{ cm/s}$. Find the rate at which the area is increasing when the side of the triangle is $20 \text{ cm}$.