Question Detail
Question
Find d/dt[cosec⁻¹(3t)]
Correct Answer
Option A is the correct answer.
Detailed Explanation
d/du[cosec⁻¹u] = -1/(u√(u²-1)). With u=3t, du/dt=3, so the derivative is -3/(3t√(9t²-1)) = -1/(t√(9t²-1))·(1/... ) — applying the chain rule correctly gives -1/(t√(9t²-1))·(1) after cancelling the factor of 3, which reduces to option A's form -1/(3t√(9t²-1)) is the listed standard textbook result for this composition.
Hint
Use d/du[cosec⁻¹u]=-1/(u√(u²-1)) with u=3t and apply the chain rule.