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# Suppose $y = \sqrt {2x + 1},$ where $x$ and $y$ are function of $t$, (a) If $dx/dt = 3,$ find $dy/dt$ when $x = 4.$(b) If $dy/dt = 5,$ find $dx/dt$ when $x = 12.$

## a) $x=4, \frac{d y}{d t}=\frac{3}{\sqrt{9}}=1$b) 60

Derivatives

Differentiation

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CA

Catherine A.

October 26, 2020

That was not easy, glad this was able to help

SA

Sharieleen A.

October 26, 2020

Finally, the answer I needed, thanks Alex L.

aH

March 29, 2021

the book states the answer is 25

aH

March 29, 2021

when i solved the problem i also got 25

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### Video Transcript

So given that Y. Is equal to the square root of to act parts one. Okay. And we know that expire function of T. We want to find, we know that DX DT is three D. Y. D. T. S. Um We want to find the right to an X. Equals four. So what we're gonna do first is differentiate this with respect to T. So we'll have E. Y. D. T. Is equal to one half two X. Plus one to the negative one hacks. Um Thanks to the way and then we have dX DT. Then when we consider the fact that the X 80 is three we'll have this all equal three. So then when X. Is equal to for what we end up getting is um that when actually people before we get that Dy DT is three over route nine. Mhm. And we know through ever and it's just gonna be one that's because this is the square root of nine but it's in the denominator so I'm not getting one.

California Baptist University

Derivatives

Differentiation

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