CBSE Class 12-science Answered

differentiate Sin^-1{2^x+1 . 3^x /1+(36)^x} w.r.t x

Asked by ADITYA MATHEW | 23 May, 2014, 07:11: AM

Expert Answer

$L e t space y equals sin to the power of minus 1 end exponent open curly brackets fraction numerator 2 to the power of x plus 1 end exponent cross times 3 to the power of x over denominator 1 plus open parentheses 36 close parentheses to the power of x end fraction close curly brackets W e space k n o w space t h a t space fraction numerator d over denominator d x end fraction open square brackets sin to the power of minus 1 end exponent x close square brackets equals fraction numerator 1 over denominator square root of 1 minus x squared end root end fraction W e space n e e d space t o space f i n d space fraction numerator d y over denominator d x end fraction : T h u s comma space fraction numerator d y over denominator d x end fraction equals fraction numerator 1 over denominator square root of 1 minus open parentheses fraction numerator 2 to the power of x plus 1 end exponent cross times 3 to the power of x over denominator 1 plus open parentheses 36 close parentheses to the power of x end fraction close parentheses squared end root end fraction cross times fraction numerator open parentheses 1 plus open parentheses 36 close parentheses to the power of x close parentheses open square brackets 2 to the power of x plus 1 end exponent cross times ln open parentheses 3 close parentheses cross times 3 to the power of x plus 3 to the power of x cross times ln open parentheses 2 close parentheses cross times 2 to the power of x plus 1 end exponent close square brackets minus open square brackets ln open parentheses 36 close parentheses cross times 3 to the power of x cross times 36 to the power of x cross times 2 to the power of x plus 1 end exponent close square brackets over denominator open parentheses 1 plus open parentheses 36 close parentheses to the power of x close parentheses squared end fraction$