dx/dt = 4+3√3 in the case of the circle with radius 4 and the equation x²+y²=16.
The method of finding an implicit function's dependent variable's derivative by differentiating each term individually, symbolizing the derivative, and then solving the resulting expression for the symbol.
Without having to solve the provided equation for y, you may use the implicit differentiation technique to determine the derivative of y with respect to x.
Because we assume that y may be written as a function of x, the chain rule must always be applied when differentiating the function y.
So, the dx/dt will be:
The circle's equation is: x² + y² = 16
Assuming that x = 2, then:
2² + y² = 16
y² = 12
y = ±√12
Hence, the first quadrant is positive:
y = √12
y = 2√3
When implicit differentiation is used, we get that:
2x dx/dt + 2y dy/dt = 16
If fracdydt = -3, as is the case, then
2(2) dx/dt - 12√3 = 16
4 dx/dt = 16 + 12√3
dx/dt = 16+12√3/4
dx/dt = 4+3√3
Therefore, dx/dt = 4+3√3 in the case of the circle with radius 4 and the equation x² + y² = 16.
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