Question Detail
Question
Find the first derivative of sec⁻¹ (5x) with respect to x?
Correct Answer
Option D is the correct answer.
Detailed Explanation
The derivative of sec⁻¹(u) with respect to x is (1 / (|u|√(u² - 1))) * du/dx.In this case, u = 5x.So, du/dx = 5.Substitute u and du/dx into the formula:d/dx (sec⁻¹(5x)) = (1 / (|5x|√((5x)² - 1))) * 5= 5 / (5|x|√(25x² - 1))= 1 / (|x|√(25x² - 1))Assuming x > 0 for simplicity (which is common in these types of problems unless specified), |x| = x.= 1 / (x√(25x² - 1)).
Hint
Recall the derivative formula for inverse secant: d/dx(sec⁻¹(u)) = u' / (|u|√(u² - 1)).