The surface area of a cube increases at a rate of $2 \ cm^2/sec$. The rate at which its volume increases when the length of its edge is $90 \ cm$ is ..... $cm^3/sec$.

$A$ kite is moving horizontally at a height of $151.5 \ m$. If the speed of the kite is $10 \ m/s$,how fast is the string being let out when the kite is $250 \ m$ away from the boy who is flying the kite? The height of the boy is $1.5 \ m$.

$A$ point moves along the arc of the parabola $y = 2x^2$. Its abscissa increases uniformly at the rate of $2 \text{ units/sec}$. At the instant the point is passing through $(1, 2)$,its distance from the origin is increasing at the rate of

If $y=5x^2+6x+6$,$x=2$,and $\Delta x=0.001$,then the value of $dy$ is:

The total revenue in Rupees received from the sale of $x$ units of a product is given by $R(x) = 3x^2 + 36x + 5$. Find the marginal revenue when $x = 5$,where marginal revenue is defined as the rate of change of total revenue with respect to the number of items sold at an instant.

Each edge of a cube is expanding at the rate of $1 \text{ cm/sec}$. Then the rate (in $\text{cc/sec}$) of change in its volume,when each of its edge is of length $5 \text{ cm}$,is