Limits, Continuity & Differentiability
Rules for Differentiation
Grade 12
Question:
<p>If <i>f</i>(<i>x</i>) = <span style='border-top:1px solid black; padding:0 0.3em;'>1 + cos<sup>2</sup>(<i>x</i><sup>2</sup>)</span>, then the value of <i>f</i>′(π/6) is</p>
<p>(a) π/6</p>
<p>(b) −π/6</p>
<p>(c) 1/6</p>
<p>(d) π/6</p>
Step-by-Step Solution
Key Concept: Use the chain rule to differentiate the composite function involving a square root and cosine.
<p><strong>Solution:</strong> Differentiate <i>f</i>(<i>x</i>) = <span style='border-top:1px solid black; padding:0 0.3em;'>1 + cos<sup>2</sup>(<i>x</i><sup>2</sup>)</span> using the chain rule. Evaluate at <i>x</i> = π/6.</p>
Correct Answer: B