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Maths-

General

Easy

Question

Let $f left parenthesis x right parenthesis equals e to the power of x comma g left parenthesis x right parenthesis equals sin to the power of negative 1 end exponent invisible function application x text and end text h left parenthesis x right parenthesis equals f left square bracket g left parenthesis x right parenthesis right square bracket comma text then end text fraction numerator h to the power of straight prime left parenthesis x right parenthesis over denominator h left parenthesis x right parenthesis end fraction$ is equal to

$e^{\sin^{- 1} x}$
$\frac{1}{\sqrt{1 - x^{2}}}$
$\sin^{- 1} x$
$\frac{1}{(1 - x^{2})}$

The correct answer is: $fraction numerator 1 over denominator square root of 1 minus x squared end root end fraction$

Given, $f left parenthesis x right parenthesis equals e to the power of x comma g left parenthesis x right parenthesis equals sin to the power of negative 1 end exponent invisible function application x$
Since, $h left parenthesis x right parenthesis equals f left square bracket g left parenthesis x right parenthesis right square bracket equals e to the power of sin to the power of negative 1 end exponent invisible function application x end exponent$
Now, $h to the power of straight prime left parenthesis x right parenthesis equals e to the power of sin invisible function application x end exponent times fraction numerator 1 over denominator square root of 1 minus x squared end root end fraction$
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow straight h to the power of straight prime left parenthesis straight x right parenthesis equals straight h left parenthesis straight x right parenthesis times fraction numerator 1 over denominator square root of 1 minus straight x squared end root end fraction end cell row cell not stretchy rightwards double arrow fraction numerator straight h to the power of straight prime left parenthesis straight x right parenthesis over denominator straight h left parenthesis straight x right parenthesis end fraction equals fraction numerator 1 over denominator square root of 1 minus straight x squared end root end fraction end cell end table$

Related Questions to study

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