Differentiate the given function. $$f ( x ) = \ln x ^ { 3 }$$
A) $\frac { x } { 3 }$
B) $\frac { 1 } { 3 x }$
C) 3x
D) $\frac { 3 } { x }$

Question

Quizplus · Accepted Answer

The differentiation of $f(x) = \ln x^3$ can be simplified using the chain rule and properties of logarithms. First, use the property that $\ln x^n = n \ln x$, so $f(x) = 3 \ln x$. Differentiating $3 \ln x$ with respect to $x$ gives $3 \cdot \frac{1}{x} = \frac{3}{x}$.

Differentiate the Given Function f(x)=ln⁡x3f ( x ) = \ln x ^ { 3 }f(x)=lnx3

Differentiate the Given Function $f ( x ) = \ln x ^ { 3 }$