Limits, Continuity & Differentiability
Derivatives of Inverse Functions
Grade 12
Question:
<p>If <span>\(y = \tan^{-1}(\sec x - \tan x)\)</span>, then <span>\(\frac{dy}{dx}\)</span> is equal to</p>
<p>(a) <span>\(2\)</span></p>
<p>(b) <span>\(-2\)</span></p>
<p>(c) <span>\(\frac{1}{2}\)</span></p>
<p>(d) <span>\(-\frac{1}{2}\)</span></p>
Step-by-Step Solution
Key Concept: Apply chain rule and differentiation of inverse trigonometric functions.
<p><strong>Solution:</strong> Differentiate using chain rule and inverse trigonometric derivative formulas.</p>
Correct Answer: d