How do you do this question? Please help. 10 points for correct answer with steps

A point (x,y) moves along a curve, (x^2+4)^2, in such a way that the y-coordinate is increasing at a rate of 3 units per second. Find the corresponding rate of change of the x-coordinate when x=1.

... y = (x^2 + 4)^2
or dy/dx = 4x (x^2 + 4)
or dx/dy = 1 / [ 4x (x^2 + 4) ]

... dy/dt = 3
or dx/dy (dy/dt) = dx/dt = 3 / [ 4x ( x^2 + 4 ) ]
or [ @ x = 1 ] dx/dt = 3 / [ 4(1) ( (1)^2 + 4 ) ] = .15

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We are given:
y = (x²+4)² and that dy/dt = 3

Differentiating implicitly with respect to time t:
dy/dt = 2(x²+4)(2x)(dx/dt)

So, for x=1 and dy/dt=3:
3 = 2(1²+4)(2·1)(dx/dt)
3 = 20(dx/dt)
3/20 = 0.15 = dx/dt            ← ANSWER


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