If $f (x) = sec x$ $f(x)=secx$ 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:

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

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