Can somebody show me the missing steps? Calculus statement soon to come...

Question

anonymous · Answer

$$\frac{ dh }{ dt }=\frac{ d({h^{1/2})}^2 }{ dt }=2h^{1/2}\frac{ d{h^{1/2}} }{ dt }$$

anonymous · Answer

Please show how they go from (2) to (3)

anonymous · Answer

There are initial conditions of t=0 and h=h* if that helps any

anonymous · Answer

chain rule

anonymous · Answer

h is height. This is a cylindrical tank problem.

anonymous · Answer

$$\frac{d}{dx}[f^2(x)]=2f(x)f'(x)$$

anonymous · Answer

why you would want to do this is not clear, but it is via the chain rule

anonymous · Answer

that's right.. Thanks

anonymous · Answer

yw

anonymous · Answer

Chemical Engineering question. I'll post the original question so you can satisfy your curiosity

anonymous · Answer

A cylindrical tank with an inside radius R and is initially filled with water to a height h*. At time t = 0, a drain opening at the bottom of the pool is opened and water is drained from the pool at a volumetric rate v(out) given by v(out)=α'h^½, where h is the height of the water level in pool at time t, and α' are constants with the appropriate units. Derive and solve the differential equation governing h(t) in terms of the parameters given above.

anonymous · Answer

@satellite73 I posted the question it your were curious why