What is the derivative of #f(x) = lnx^3#?

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Answer 1 · 2018-03-09T18:45:01

#d/dx(ln(x^3))=3/(x)#

We have:

#f(x)=ln(x^3)#

Remember the chain rule and the power rule and the natural log rule.

#d/dx(lnx)=1/x#

#d/dx(x^n)=nx^(n-1)# where #n# is a constant.

#d/dx(f(g(x)))=f'(g(x))*g'(x)#

Therefore,

#=>d/dx(ln(x^3))=1/(x^3)*d/dx(x^3)#

#=>d/dx(ln(x^3))=1/(x^3)*3x^2#

#=>d/dx(ln(x^3))=1/(cancel(x^2)*x)*3cancel(x^2)#

#=>d/dx(ln(x^3))=1/(x)*3#

#=>d/dx(ln(x^3))=3/(x)#

Answer 2 · 2018-03-09T19:16:38

#3/x#

#f(x) = lnx^3 = 3lnx#

So #f'(x) = 3 * 1/x = 3/x#