Find $\frac { d } { d x } \left( \ln \left( x ^ { 3 } e ^ { x } \right) \right)$ .
A) $\frac { 3 } { x } + 1$
B) $\frac { 3 } { x }$
C) $\frac { 1 } { x ^ { 3 } e ^ { x } }$
D) $\frac { 3 x + e ^ { x } } { x ^ { 3 } e ^ { x } }$

Question

Quizplus · Accepted Answer

The derivative of $\ln(x^3e^x)$ can be simplified using the properties of logarithms as $\ln(x^3) + \ln(e^x)$, which differentiates to $\frac{3}{x} + 1$.

Find ddx(ln⁡(x3ex))\frac { d } { d x } \left( \ln \left( x ^ { 3 } e ^ { x } \right) \right)dxd​(ln(x3ex))

Find $\frac { d } { d x } \left( \ln \left( x ^ { 3 } e ^ { x } \right) \right)$