$\text { Find an equation of the tangent line to the graph of } y = \ln \left( x ^ { 3 } \right) \text { at the point } ( 1,0 ) \text {. }$
A) $y = 3 ( x - 1 ) + 1$
B) $y = 3 ( x + 1 )$
C) $y = 3 ( x - 1 )$
D) $y = x - 1$
E) $y = x - 3$

Question

$\text { Find an equation of the tangent line to the graph of } y = \ln \left( x ^ { 3 } \right) \text { at the point } ( 1,0 ) \text {. }$ 
A) $y = 3 ( x - 1 ) + 1$
B) $y = 3 ( x + 1 )$
C) $y = 3 ( x - 1 )$
D) $y = x - 1$
E) $y = x - 3$

Quizplus · Accepted Answer

To find the equation of the tangent line, we first need the derivative of $y = \ln(x^3)$. Using the chain rule, the derivative is $y' = \frac{3}{x}$. At $x = 1$, $y' = 3$. The point given is (1,0), so the equation of the tangent line is $y - 0 = 3(x - 1)$, which simplifies to $y = 3(x - 1)$.