Let $x$ and $y$ be the sides of two squares such that $y = x - x^2$. The rate of change of the area of the second square with respect to the area of the first square is

The $x$-coordinate changes on the curve $y=3x^5+15x-8$ at the rate of $\frac{1}{5} \text{ units/sec}$. If $A(x_1, y_1)$ and $B(x_2, y_2)$ are the points on the curve at which the $y$-coordinate changes at the rate of $6 \text{ units/sec}$, then the slope of $AB$ is:

The edge of a cube is decreasing at the rate of $0.04 \ cm/sec$. If the edge of the cube is $10 \ cm$,then the rate of decrease of the surface area of the cube is...

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

An object is moving in the clockwise direction around the unit circle $x^2+y^2=1$. As it passes through the point $\left(\frac{1}{2}, \frac{\sqrt{3}}{2}\right)$,its $y$-coordinate is decreasing at the rate of $3 \text{ units/sec}$. The rate at which the $x$-coordinate changes at this point is

The rate of change of the volume of a sphere with respect to its surface area,when the radius is $5 \ m$ is