If $pv = 81$,then $\frac{dp}{dv}$ at $v = 9$ is equal to

$A$ particle is moving in a straight line. Its displacement at time $t$ is given by $s = -4t^2 + 2t$. Then its velocity and acceleration at time $t = \frac{1}{2} \text{ s}$ are:

The sides of an equilateral triangle are increasing at the rate of $2 \text{ cm s}^{-1}$. How fast does its area increase when its side is $10 \text{ cm}$?

The points on the ellipse $16x^{2} + 9y^{2} = 400$ at which the ordinate decreases at the same rate at which the abscissa increases are given by:

$A$ point is in motion along a hyperbola $y = \frac{10}{x}$ such that its abscissa $x$ increases uniformly at a rate of $1 \text{ unit/s}$. Find the rate of change of its ordinate when the point passes through $(5, 2)$.

The rate of change of the radius of a sphere is $0.1 \ cm/s$. Find the rate of change of its surface area when its radius is $200 \ cm$.