Question

Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt. y = √x , (a) Find dy/dt, given x = 4 and dx/dt = 5. dy/dt = _______ (b) Find dx/dt, given x = 49 and dy/dt = 3. dx/dt = __________

Answer 1

Answer: a)
`(5)/(4)` b) 42

Explanation:

Since we have given that

`y=√(x)`

We need to find the

a) (a) Find dy/dt, given x = 4 and dx/dt = 5.

`(dy)/(dt)=(1)/(2√(x))(dx)/(dt)\\\\(dy)/(dt)=(1)/(2√(4))* 5\\\\(dy)/(dt)=(1)/(4)* 5\\\\(dy)/(dt)=(5)/(4)`

(b) Find dx/dt, given x = 49 and dy/dt = 3.

`(dy)/(dt)=(1)/(2√(x))(dx)/(dt)\\\\3=(1)/(2√(49))* (dx)/(dt)\\\\3=(1)/(14)* (dx)/(dt)\\\\(dx)/(dt)=14* 3=42`

Hence, a)
`(5)/(4)` b) 42