Question Detail
Question
What is d/dx (tan-1(ax))?
Correct Answer
Option D is the correct answer.
Detailed Explanation
To find the derivative of tan-1(ax), we use the chain rule for inverse trigonometric functions.The derivative of tan-1(u) with respect to x is (1 / (1 + u2)) * du/dx.In this case, let u = ax.Then, du/dx = d/dx (ax) = a.Substitute these into the formula:d/dx (tan-1(ax)) = (1 / (1 + (ax)2)) * a= a / (1 + a2x2).
Hint
Recall the derivative of the arctangent function: d/dx(tan-1(u)) = u'/(1+u2).