calculus help

[dolphin6]

evaluate dy/dt for the function at the point
ysquare root x+1=12;dx/dt=8,x=15,y=3

 

[stapel]

Your formatting is ambiguous, so little specific can be said. But, in general, you need to differentiate implicitly with respect to "t", and then plug in all the given values. Solve for the only remaining variable, "dy/dt".

Eliz.

 

[dolphin6]

reply

could you work it out

 

[stapel]

Please review my earlier reply, wherein it was explained why this would be quite difficult (even if I customarily provided fully-worked solutions, which I don't).

Then please reply with clarification, using formatting as explained in the links in the "Forum Help" pull-down menu at the very top of the page. When you reply, please show how far you have gotten in following the step-by-step instructions.

Thank you.

Eliz.

 

[Unco]

G'day, Dolphin6.

Evaluate \(\displaystyle \frac{dy}{dt}\) for the function at the point
\(\displaystyle \Large y\sqrt{ x + 1} = 12 ; \, \frac{dx}{dt} = 8, \, x = 15, \, y = 3\)

If that is correct, make y the subject of the equation and differentiate to find dy/dx.

Then apply the chain rule: dy/dt = dy/dx * dx/dt, where you have been given dx/dt, and finally substitute the given values for x and y.

 

[pka]

Unco, you have the right idea, but went too far.

\(\displaystyle y\sqrt {x + 1} = 12\; \Rightarrow (dy/dt)\sqrt {x + 1} + \frac{{y(dx/t)}}{{2\sqrt {x + 1} }} = 0\)

\(\displaystyle (dy/dt)\sqrt {15 + 1} + \frac{{3(8)}}{{2\sqrt {15 + 1} }} = 0\)

Now solve for \(\displaystyle (dy/dt)\)!