Question

consider y = √x,find dy/dt,given x=9 and dx/dt=3

Answer 1

Differentiate implicitly with respect to t.

let y = x^(1/2)

dy/dt = (1/2)x^(-1/2) dx/dt

now substitute for x, y, and dx/dt, and find dy/dt.

Answer 2

y = √(x) = x^(1/2)
dy/dt = (1/2)(x^(-1/2)) dx/dt = (1/2)(1/√(x)) dx/dt = (1/2√(x)) dx/dt
dy/dt = 1/(2√(x)) dx/dt

Plug in given values.

dy/dt = 1/(2√(9))*(3)
dy/dt = 3/(2(±3))
dy/dt = 3/(±6)
dy/dt = ±1/2

@Easyaspi314, you mind checking my work on the last bit? I'm a little confused how I could have gotten a ± value for a numerical derivative...

Answer 3

Correct..except at the end, sqrt(9) = 3 only, not + and - 3.
So your answer will change to 1/2 only.

Answer 4

Got it, thank you very much! The answer would indeed be dy/dt = 1/2 then.

Answer 5

Agree.

Answer 6

thanks all