Question

if f(x) = secx
then find
f''(pi by 4 )=?

Answer 1

The answer is given below :

f(x) = secx .....(i)

Differentiating both sides of (i), we get -

f'(x) = secx tanx .....(ii)

Again, differentiating both sides of (ii), we get -

f"(x) = secx (d/dx)(tanx) + tanx (d/dx)(secx)

= secx (sec²x) + tanx (secx tanx)

= sec³x + secx tan²x

Thus,

f"(π/4)

= (sec π/4)³ + (sec π/4) (tan π/4)²

= (√2)³ + (√2) (1)²

= 2√2 + √2

= 3√2

Thank you for your question.