Determine dh/dt

Question

Given h = √(100−x²) and x = 1.2t

Answer 1

Finding dh/dt (since x is a function of t), requires the use of the chain rule.

dh/dt = d(√(100−x²))/dt = 1/2(100 - x²)^-1/2 • (-2x) • dx/dt

Since x = 1,2t, dx/dt = 1.2

dh/dt = 1/2(100 - x²)^-1/2 • (-2x) • dx/dt

dh/dt = 1/2(100 - (1.2t)²)^-1/2 • (-2(1.2t)) • (1.2)

dh/dt = (-1.44t)(100 - 1.44t²)^-1/2

Answer 2

dh/dt = (dh/dx)(dx/dt)

But dh/dx = -x(100 - x²)^-1/2 and dx/dt = 1.2

==> dh/dt = -1.2x(100 - x²)^-1/2 = -1.44t (100 - (1.2t)²)^-1/2