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) is d/dx (sec-1(u)) = (1 / (|u|√(u² - 1))) * du/dx.Here, u = 5x, so du/dx = 5.Substitute these into the formula:d/dx (sec-1(5x)) = (1 / (|5x|√((5x)² - 1))) * 5= (1 / (5|x|√(25x² - 1))) * 5= 1 / (|x|√(25x² - 1)).Assuming x > 0 (as is common for these problems unless otherwise specified in options), |x| = x.So, the derivative is 1 / (x√(25x² - 1)).
Hint
Recall the differentiation formula for inverse secant function: d/dx (sec-1(u)) = u' / (|u|√(u²-1)).