For the circle centered at the origin with radius 4 and equation x^2+y^2=16, find dx/dt at the first quadrant point where x=2 if dy/dt=-3 at that instant.

Using implicit differentiation, it is found that:

The equation of the circle is:

We are given x = 2, then:

First quadrant, thus, positive:

Applying implicit differentiation, we have that:

We are given that , then:

A similar problem is given at link

dx/dt = 12

Step-by-step explanation:

Given the  equation of a circle expressed as:

x²+y² = 16

Differentiate the expression with respect to x

2x dx/dt + 2y dy/dt = 0

Given

x = 2

dy/dt = 3

Required

dx/dt

Substitute the given parameters into the resulting differential equation

2x dx/dt + 2y dy/dt = 0

2 dx/dt + 2(4) (-3) = 0

y = 4 since the radius is 3,

2 dx/dt - 24 = 0

2 dx/dt = 24

dx/dt = 24/2

dx/dt = 12