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 dx/dt = 3 and x = 4. dy/dt = (b) Find dx/dt, given x = 25 and dy/dt = 2. dx/dt =

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 dx/dt = 3 and x = 4. dy/dt =  (b) Find dx/dt, given x = 25 and dy/dt = 2. dx/dt =

anonymous · Answer

It means derivative of y, right?

anonymous · Answer

Ok, so when I find the derivative I get 1/2x^-1/2... but I don't know what to do next

dumbcow · Answer

its the chain rule
$$\frac{dy}{dt} = \frac{dy}{dx}*\frac{dx}{dt}$$

dumbcow · Answer

$$= \frac{1}{2\sqrt{4}}*3$$

anonymous · Answer

Ok. I understand that. You plugged 4 into the derivative. Then we multiply and get $$3/2\sqrt{4}$$ right? And that's the answer?

dumbcow · Answer

yes well simplify it to 3/4

anonymous · Answer

Ok. Wow, that's not that hard. Thanks.

dumbcow · Answer

yw

anonymous · Answer

For b my book says the answer should be 20 but I'm getting 1/10.

dumbcow · Answer

$$2 = \frac{1}{2\sqrt{25}}*\frac{dx}{dt}$$

dumbcow · Answer

see why it is 20

anonymous · Answer

Oops thanks.

dumbcow · Answer

dont switch the dx and dy , always start with
$$\frac{dy}{dt} = \frac{dy}{dx}*\frac{dx}{dt}$$
then substitute given values

anonymous · Answer

Yeah, I understand. I got dx/dt by itself but I lost the two somewhere so I didn't divide by it.

anonymous · Answer

Thank you. =)