Question

A particle is moving along the curve whose equation is
(xy3)/(1+y^2) =8/5
Assume that the x-coordinate is increasing at the rate of 6 units/s when the particle is at the point
( 1,2).
(a) At whate is the y-coordinate of the pointchanging at that instant?
(b) Is the particle rising or falling at that instant?

Answer 1

@ranga help

Answer 2

Do implicit differentiation of the equation with respect to time t first.
Use quotient rule, product rule and power rule.

Then substitute x = 1, y = 2, dx/dt = 6 and solve for dy/dt. That answers a)

For b) if the slope of the curve dy/dx at the point (1,2) is positive the particle is rising. If it is negative, the particle is falling.

Answer 3

i made a mistake it's xy^3 not xy3