If #f(x)=secx# then calculate #f''(pi/3)#?

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Answer 1 · 2017-09-29T15:24:34

# f''(pi/3) = 14 #

We have:

# f(x) = secx #

Differentiate wrt #x#:

# f'(x) = secxtanx #

Differentiate wrt #x# applying the product rule:

# f''(x) = secx(d/dxtanx) + (d/dxsecx)tanx#
# \ \ \ \ \ \ \ \ \ \ \ = secx(sec^2x) + (secxtanx)tanx#
# \ \ \ \ \ \ \ \ \ \ \ = sec^3x + secxtan^2x#

When #x=pi/3=> tanx=sqrt(3)#, #secx=2#, And so:

# f''(pi/3) = (2)^3 + (2)(3) = 14 #