What is the derivative of sec 2 (tan -1 x) with respect to x? (sec 2

| What is the derivative of sec2 (tan-1 x) with respect to x?

A. 2x

B. x2 + 1

C. x + 1

D. x2

Right Answer is: A

SOLUTION

(sec2 (tan-1x))

2sec(tan-1x)(sec(tan-1x)tan(tan-1x)).1/1+x2

[(sec2x)=2secx(secxtanx)]

tan-1x=t

2 sec(t)(sect)x.1/1+x2

2sec2t.x/1+x2

2(1+tan2(tan-1x)).x/1+x2

2(1+x2).x/1+x2=2x

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