differentiate

Asked by Rajeev | 19th Jul, 2015, 07:36: PM

Expert Answer:

1. C o n s i d e r space t h e space g i v e n space squared f u n c t i o n y equals sin to the power of negative 1 end exponent open parentheses fraction numerator 2 to the power of x plus 1 over denominator 1 plus 4 to the power of x end fraction close parentheses T a k i n g space sin e space o n space b o t h space t h e space s i d e s comma space w e space h a v e comma sin y equals fraction numerator 2 to the power of x plus 1 over denominator 1 plus 4 to the power of x end fraction... left parenthesis 1 right parenthesis rightwards double arrow sin y open parentheses 1 plus 4 to the power of x close parentheses equals 2 to the power of x plus 1 D i f f e r e n t i a t i n g space t h e space a b o v e space e q u a t i o n space w i t h space r e s p e c t space t o space x comma space w e space h a v e comma sin y cross times 4 to the power of x cross times log 4 plus open parentheses 1 plus 4 to the power of x close parentheses cross times cos y cross times fraction numerator d y over denominator d x end fraction equals 2 to the power of x cross times l o g 2 rightwards double arrow open parentheses 1 plus 4 to the power of x close parentheses cross times c o s y cross times fraction numerator d y over denominator d x end fraction equals 2 to the power of x cross times l o g 2 minus s i n y cross times 4 to the power of x cross times l o g 4 rightwards double arrow fraction numerator d y over denominator d x end fraction equals fraction numerator 2 to the power of x cross times log 2 minus sin y cross times 4 to the power of x cross times log 4 over denominator open parentheses 1 plus 4 to the power of x close parentheses cross times c o s y end fraction rightwards double arrow fraction numerator d y over denominator d x end fraction equals fraction numerator 2 to the power of x cross times l o g 2 minus fraction numerator 2 to the power of x plus 1 over denominator 1 plus 4 to the power of x end fraction cross times 4 to the power of x cross times l o g 4 over denominator open parentheses 1 plus 4 to the power of x close parentheses cross times square root of 1 minus open parentheses fraction numerator 2 to the power of x plus 1 over denominator 1 plus 4 to the power of x end fraction close parentheses squared end root end fraction rightwards double arrow fraction numerator d y over denominator d x end fraction equals fraction numerator begin display style fraction numerator 2 to the power of x cross times log 2 over denominator open parentheses 1 plus 4 to the power of x close parentheses end fraction end style minus fraction numerator 2 to the power of x plus 1 over denominator open parentheses 1 plus 4 to the power of x close parentheses squared end fraction cross times 4 to the power of x cross times l o g 4 over denominator square root of 1 minus open parentheses fraction numerator 2 to the power of x plus 1 over denominator 1 plus 4 to the power of x end fraction close parentheses squared end root end fraction
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Answered by Vimala Ramamurthy | 20th Jul, 2015, 09:26: AM

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