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Applying implicit differentiation, it is found that dy/dt when y=π/4 is of:
a-) -√2 / 2.
<h3>What is implicit differentiation?</h3>Implicit differentiation is when we find the derivative of a function relative to a variable that is not in the definition of the function.
In this problem, the function is:
xcos(y) = 2.
The derivative is relative to t, applying the product rule, as follows:
Since dx/dt=−2, we have that:
When y = π/4, x is given by:
xcos(y) = 2.
Hence:
Since cot(pi/4) = 1, we have that:
Which means that option a is correct.
More can be learned about implicit differentiation at brainly.com/question/25608353
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