Find the value of d/dx(root x+ 1/root x)2

Asked by Anil | 31st May, 2017, 12:26: PM

Expert Answer:

begin mathsize 16px style fraction numerator space straight d over denominator dx end fraction open parentheses fraction numerator square root of straight x plus 1 over denominator square root of straight x end fraction close parentheses squared
equals fraction numerator space straight d over denominator dx end fraction open square brackets fraction numerator open parentheses square root of straight x plus 1 close parentheses over denominator straight x end fraction squared close square brackets
equals fraction numerator space straight d over denominator dx end fraction open square brackets fraction numerator open parentheses straight x plus 2 square root of straight x plus 1 close parentheses over denominator straight x end fraction close square brackets
equals fraction numerator space straight d over denominator dx end fraction open square brackets 1 plus fraction numerator 2 over denominator square root of straight x end fraction plus 1 over straight x close square brackets
equals 0 plus 2 open parentheses negative 1 half close parentheses straight x to the power of negative 3 divided by 2 end exponent minus 1 over straight x squared
equals negative 1 over straight x to the power of 3 divided by 2 end exponent minus 1 over straight x squared end style

Answered by Rebecca Fernandes | 24th Nov, 2017, 11:50: AM