If y = sec (tan^-1 x), then dy/dx at x = 1 is equal to

$fraction numerator 1 over denominator square root of 2 end fraction$
$1 half$

1

$square root of 2$

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Solution

fraction numerator 1 over denominator square root of 2 end fraction

space straight y space equals space sec space left parenthesis tan to the power of negative 1 end exponent space straight x right parenthesis dy over dx space equals space sec space left parenthesis tan to the power of negative 1 end exponent space straight x right parenthesis space tan space left parenthesis tan to the power of negative 1 end exponent space straight x right parenthesis fraction numerator 1 over denominator 1 plus straight x squared end fraction right enclose dy over dx end enclose subscript straight x space equals 1 end subscript space equals space square root of 2 space straight x space 1 space straight x space 1 half space equals space fraction numerator 1 over denominator square root of 2 end fraction

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