CBSE

MATHEMATICS · Multi-part · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Let

h(x)=\cot\bigl(\sqrt{x}\,\bigr)

for

x>0

. (1) Determine an explicit expression for

h'(x)

in terms of elementary trigonometric functions of

\sqrt{x}

and powers of

x

. (2) Compute

h''(x)

and simplify as far as possible. (3) Evaluate

h''\!\left(\dfrac{\pi^{2}}{4}\right)

exactly.

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