Consider the function defined for all real for which the expression is meaningful.

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

Problem

Consider the function

f(x)=\tan(5x)

defined for all real

x

for which the expression is meaningful. (1) Calculate the second derivative

f''(x)

and express your answer in terms of

\tan(5x)

and

\sec(5x)

only. (2) Evaluate

f''\!\left(\dfrac{\pi}{5}\right)

exactly.