The radius of a circle is increasing at the rate of $0.7 \, cm/s$. What is the rate of increase of its circumference?

If a man of height $1.8 \ m$ is walking away from the foot of a light pole of height $6 \ m$ with a speed of $7 \ km/h$ on a straight horizontal road,then the rate of change of the length of his shadow is (in $km/h$):

$A$ particle moves along a straight line according to the law $s=16-2t+3t^{3}$,where $s$ metres is the distance of the particle from a fixed point at the end of $t$ seconds. The acceleration of the particle at the end of $2 \ s$ is

The rate of change of the area of a sphere with respect to its radius, when the radius is $6 \text{ cm}$, is . . . . . . . (in $\pi$)

The total cost $C(x)$ in Rupees associated with the production of $x$ units of an item is given by $C(x) = 0.007x^{3} - 0.003x^{2} + 15x + 4000$. Find the marginal cost when $17$ units are produced.

The volume of a spherical balloon is increasing at the rate of $40 \ cm^3/\min$. The rate of change of the surface area of the balloon at the instant when its radius is $8 \ cm$ is ........ $cm^2/\min$.