Word problem Derivative of Distance formula Super hard. Please help.

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SUMMARY

The discussion centers on a calculus problem involving the derivative of the distance formula as a point P moves along the curve defined by the equation y=√x. Specifically, the problem requires determining how fast the distance between point P and the fixed point (2,0) is changing when x=3 and increasing at a rate of 40 units/s. The distance formula is applied to find the relationship between the coordinates of P and the fixed point, leading to the need for differentiation to solve the problem.

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  • Familiarity with the distance formula in a Cartesian coordinate system
  • Knowledge of implicit differentiation techniques
  • Ability to interpret rates of change in relation to motion
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Word problem Derivative of Distance formula... Super hard. Please help.

Homework Statement



A point P is moving along the cruve whose equation is y=√x. Suppose that x is increasing
at the rate of 40 units/s when x=3. How fast is the distance between p and the point (2,0) changing\
at that instant?


Homework Equations


Distance forumula


The Attempt at a Solution


Not even posting it... Its completely wrong


Can you please show me how to do this? Show your work please.

Thanks you.
 
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Sorry I meant to say curve... not cruve.
 


Let's call the distance between P and (2,0) as s and P has the coordinates (x,y).

What is the distance between P and (2,0) ? (Use your distance formula here)
 


i got it
 

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