Question Detail
Question
The derivative of cosec⁻¹(5x) with respect to x is:
Correct Answer
Option B is the correct answer.
Detailed Explanation
The derivative of cosec⁻¹(u) with respect to x is given by -u' / (|u|√(u²-1)).In this case, u = 5x, so the derivative of u with respect to x (u') is 5.Substitute u and u' into the formula:d/dx(cosec⁻¹(5x)) = -5 / (|5x|√((5x)²-1))= -5 / (5|x|√(25x²-1))= -1 / (|x|√(25x²-1)).Assuming x > 0 (as is common in these contexts unless specified), |x| = x.So, the derivative is -1 / (x√(25x²-1)). This matches option B.
Hint
Recall the derivative formula for cosec⁻¹(u) and apply the chain rule. Remember the absolute value in the denominator.