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How do you find the derivative of #(ln(x^(2)+3))^(3)#?

1 Answer

Shwetank Mauria

Jun 19, 2016

#(df)/(dx)=(6x(ln(x^2+3))^2)/(x^2+3)#

Explanation:

Here #f(x)=(g(x))^3#, where #g(x)=ln(h(x))# and #h(x)=x^2+3#

According to chain rule #(df)/(dx)=(df)/(dg)xx(dg)/(dh)xx(dh)/(dx)#

Hence #(df)/(dx)=3(ln(x^2+3))^2xx1/(x^2+3)xx2x#

= #(6x(ln(x^2+3))^2)/(x^2+3)#

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