Assume that x and y are both differentiable functions of t and find the required vaules of dy/dt and dx/dt
Equation:
y= √x
Find:
a. dy/dt when x=4
b. dx/dt when x=25
Given:
a. dx/dt=3
b. dy/dt=2
Thanks.
\(y=\sqrt x\\ y=x^{0.5}\\ \frac{dy}{dt}=0.5x^{-0.5}\cdot \frac{dx}{dt}\\ \frac{dy}{dt}=\frac{1}{2\sqrt x}\cdot \frac{dx}{dt}\\ When\;\;x=4\\ \frac{dy}{dt}=\frac{1}{4}\cdot \frac{dx}{dt}\\\)
I could have done that more simply . Oh well, too bad.
a)
\(Since\;\; \frac{dx}{dt}=3\;\;then\\ \frac{dy}{dt}=\frac{3}{4}\\~\\ \text {that is when x=4} \)
You can do the other one. :)