A particle moves along the curve `y=x^(3/2)` in the first quadrant in such a way that its distance from the origin increases at the rate of `11` units per second. Then the value of `dx/dt` when `x=3` is given by

Explanation

Here, `y = x^(3/2)`

`=>y^2 = x^3`

Now, distance from origin is given by,

`d = sqrt(x^2+y^2)`

`=> d = sqrt(x^2+x^3)`

`=> d = xsqrt(1+x)`

Now, differentiating both sides w.r.t. x

`=> (dd)/dx = sqrt(1+x)+x*1/2(1/sqrt(1+x))`

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