Derivatives-Problem of rate of change I'm studying applications of derivatives and I have the following problem about rate of change: A raindrop falls over a surface and generated waves of circular form such that the rate of change of the radius of the wave its 636.36 ft/s and expands along 1,1s. Find the area of the circle of maximum radius. My approach: let's call r the radius then the hypothesis means upsilon=dr/dt=636.36ft/s. By physics we have r=upsilont then r=636.36∗1,1=700ft is the maximum radius. Then A=pi∗r^2=pi∗(700)^2=1539380.40ft^2.

What is the derivative of the work function?

How to use implicit differentiation to find ${\displaystyle \frac{dy}{dx}}$ given ${\displaystyle 3x^2+3y^2=2}$?

How to differentiate $y=\log <!--\; \; -->x^2$?

The solution of a differential equation y′′+3y′+2y=0 is of the form
A) $c_1{e}^x+c_2{e}^{2x}$
B) $c_1{e}^{-<!--\; -\; -->x}+c_2{e}^{3x}$
C) $c_1{e}^{-<!--\; -\; -->x}+c_2{e}^{-<!--\; -\; -->2x}$
D) $c_1{e}^{-<!--\; -\; -->2x}+c_2{2}^{-<!--\; -\; -->x}$

How to find instantaneous velocity from a position vs. time graph?

How to implicitly differentiate ${\displaystyle \sqrt{xy}=x-2y}$?

What is 2xy differentiated implicitly?

How to find the sum of the infinite geometric series given ${\displaystyle 1+\frac{2}{3}+\frac{4}{9}+...}$?

Look at this series: 1.5, 2.3, 3.1, 3.9, ... What number should come next?
A. 4.2
B. 4.4
C. 4.7
D. 5.1

What is the derivative of ${\displaystyle \frac{x+1}{y}}$?

How to find the sum of the infinite geometric series 0.9 + 0.09 + 0.009 +…?

How to find the volume of a cone using an integral?

What is the surface area of the solid created by revolving ${\displaystyle f\left(x\right)=e^{2-x},x\in [1,2]}$ around the x axis?

How to differentiate ${\displaystyle x^{\frac{2}{3}}+y^{\frac{2}{3}}=4}$?

The differential coefficient of $\sec \left({\tan }^{-1}\left(x\right)\right)$.