Calculate $y ^ { \prime }$.
$$y = \frac { e ^ { x } } { x ^ { 3 } }$$
Select the correct answer.
A)
$y ^ { t } = e ^ { x } \left( \frac { x - 1 } { x ^ { 5 } } \right)$
B) $y ^ { t } = e ^ { x } \left( \frac { x + 3 } { x ^ { 4 } } \right)$
C) $y ^ { t } = \frac { e ^ { x } } { 3 x }$
D) $y ^ { t } = e ^ { x } \left( \frac { x - 3 } { x ^ { 4 } } \right)$
E)
$y ^ { t } = e ^ { x } \left( \frac { x - 3 } { 3 x } \right)$

Question

Quizplus · Accepted Answer

The derivative is found using the quotient rule: $(\frac{u}{v})' = \frac{u'v - uv'}{v^2}$. Here, $u = e^x$ and $v = x^3$. So, $u' = e^x$ and $v' = 3x^2$. Applying the quotient rule gives $y' = \frac{e^x \cdot x^3 - e^x \cdot 3x^2}{x^6} = e^x \left(\frac{x - 3}{x^4}\right)$.

Calculate y′y ^ { \prime }y′ y=exx3y = \frac { e ^ { x } } { x ^ { 3 } }y=x3ex​

Calculate $y ^ { \prime }$ $y = \frac { e ^ { x } } { x ^ { 3 } }$