Derivative as rate of change

Derivative as rate measure and maximise minimise based on constraints

If the rate of change of volume of a sphere is the same as rate of change of its radius,then radius,is equal to

Find the rate at which the function y=x^(2) sin x is changing with respect to x when x=pi . For any x, the instantaneous rate of change in the derivative,

Derivative as a Rate Measurer

The radius of spherical bubble is changing with time. The rate of change of its volume is given by :

Assertion : The rate of reaction is the rate of change of concentration of a reactant or a product. Reason : Rate of reaction remians constant during the complete reaction.

For curve y=(x^(2))/(2)-2x+5 the rate of change of y is twice the rate of change of x ,then value of x is

For curve y=(x^(2))/(2)-2x+5, the rate of change of y is twice the rate of change of x , then value of x is