Limits, Continuity & Differentiability
Rules for Differentiation
Grade 12
Question:
<p>The value of <span style='display:inline-block; position:relative; bottom:0.25em;'>d</span>/<span style='display:inline-block; position:relative; bottom:-0.25em;'>dx</span> <span style='border-top:1px solid black; padding:0 0.3em;'><span style='display:block;'>tan<sup>2</sup>(x/(1-tan<sup>2</sup>x))</span><span style='display:block;'>cot 3x</span></span> is</p>
<p>(a) tan 2x tan x</p>
<p>(b) tan 3x tan x</p>
<p>(c) sec<sup>2</sup> x</p>
<p>(d) sec x tan x</p>
Step-by-Step Solution
Key Concept: Apply chain rule and trigonometric identities to simplify the derivative of composite trigonometric functions.
<p><strong>Solution:</strong> Use the chain rule and product rule for differentiation. Simplify the expression inside the derivative and apply trigonometric identities to obtain sec<sup>2</sup> x.</p>
Correct Answer: C