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How do you find the derivative of # sqrt(x)/(x^3+1)#?

1 Answer

Shwetank Mauria

Jul 4, 2016

#(df)/(dx)=(1-5x^3)/(2sqrtx(x^3+1)^2)#

Explanation:

As #f(x)=sqrtx/(x^3+1)#, using quotient rule,

#(df)/(dx)=(d/(dx)sqrtx xx (x^3+1)-d/(dx)(x^3+1)xx sqrtx)/(x^3+1)^2#

= #(1/(2sqrtx)xx(x^3+1)-3x^2 xx sqrtx)/(x^3+1)^2#

= #(x^3+1-6x^3)/(2sqrtx(x^3+1)^2)#

= #(1-5x^3)/(2sqrtx(x^3+1)^2)#

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