If a spherical balloon has a variable diameter $3x + \frac{9}{2}$,then find the rate of change of its volume with respect to $x$.

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

If the surface area of a cube is increasing at a rate of $3.6 \text{ cm}^2/\text{sec}$,while maintaining its shape,then the rate of change of its volume (in $\text{cm}^3/\text{sec}$),when the length of a side of the cube is $10 \text{ cm}$,is:

If a particle moves in a straight line according to the law $x = a \sin (\sqrt{\lambda} t + b)$, then the particle will come to rest at two points whose distance is [symbols have their usual meaning]

$A$ point $P$ is moving on the curve $x^3 y^4 = 2^7$. The $x$-coordinate of $P$ is decreasing at the rate of $8 \text{ units per second}$. When the point $P$ is at $(2, 2)$, the $y$-coordinate of $P$:

If the radius of a spherical balloon is increasing at the rate of $5 \text{ inch/min}$, then the rate at which the volume increases (in $\text{cubic inches/min}$) when the radius is $10 \text{ inches}$ is: (in $\pi$)