Question

From interactmath.com (free practice problems)

Spose that a dimension x and the area A=4x^2 are differentiable functions of t.

Write an equation that relates dA/dt to dx/dt.

Answer 1

x = f(t)
A = 4x^2

dA/dt = 8x*dx/dt

?

Answer 2

yep, just an implicit derivative :)

Answer 3

A' = 8x x'

wrt.t = dA/dt = 8x * dx/dt