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How do you find the derivative of # f(x)= (x+1)/sqrtx#?

1 Answer

Jul 7, 2016

#f'(x)=1/2(x^(-1/2)-x^(-3/2)),#

OR, #f'(x)=1/2{1/sqrtx-1/(x*sqrtx)}=1/2{(x-1)/(xsqrtx)}=(x-1)/(2xsqrtx).#

Explanation:

#f(x)=(x+1)/sqrtx=x/sqrtx+1/sqrtx=sqrtx+1/sqrtx=x^(1/2)+x^(-1/2).#

Therefore, #f'(x)=1/2*x^(1/2-1)+(-1/2)*x^(-1/2-1)#
#:. f'(x)=1/2(x^(-1/2)-x^(-3/2)),#

OR, #f'(x)=1/2{1/sqrtx-1/(x*sqrtx)}=1/2{(x-1)/(xsqrtx)}=(x-1)/(2xsqrtx).#

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