| What is the derivative of sec

^{2}(tan^{-1}x) with respect to x?A. 2x

B. x^{2} + 1

C. x + 1

D. x^{2}

### Right Answer is: A

#### SOLUTION

(sec^{2} (tan^{-1}x))

→2sec(tan^{-1}x)(sec(tan^{-1}x)tan(tan^{-1}x)).1/1+x^{2}

^{[}(sec^{2}x)=2secx(secxtanx)]

tan^{-1}x=t

→2 sec(t)(sect)x.1/1+x^{2}

→2sec^{2}t.x/1+x^{2}

→2(1+tan^{2}(tan^{-1}x)).x/1+x^{2}

→2(1+x^{2}).x/1+x^{2}=2x