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How do you find the derivative of #f(x)=3sqrt(x)-(2/sqrt(x))#?

1 Answer

Jun 29, 2016

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

In Radicals,
#f'(x)=(3x+2)/(2xsqrtx).#

Explanation:

#f(x)=3sqrtx-2/sqrtx=3*x^(1/2)-2*x^(-1/2)#.
#f'(x)=3*{(x)^(1/2)}'-2*{x^(-1/2)}'=3*1/2*x^(1/2-1)-2(-1/2)*x^(-1/2-1)=3/2*x^(-1/2)+x^(-3/2)#

Using Radicals,
#f'(x)=3/(2sqrtx)+1/(xsqrtx)=(3x+2)/(2xsqrtx).#

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