Find the derivative of the function.
-$$y = \frac { x ^ { 2 } - 3 x + 2 } { x ^ { 7 } - 2 }$$
A) $y ^ { \prime } = \frac { - 5 x ^ { 8 } + 19 x ^ { 7 } - 14 x ^ { 6 } - 4 x + 6 } { \left( x ^ { 7 } - 2 \right) ^ { 2 } }$
B) $y ^ { \prime } = \frac { - 5 x ^ { 8 } + 18 x ^ { 7 } - 13 x ^ { 6 } - 4 x + 6 } { \left( x ^ { 7 } - 2 \right) ^ { 2 } }$
C) $y ^ { \prime } = \frac { - 5 x ^ { 8 } + 18 x ^ { 7 } - 14 x ^ { 6 } - 4 x + 6 } { \left( x ^ { 7 } - 2 \right) ^ { 2 } }$
D) $y ^ { \prime } = \frac { - 5 x ^ { 8 } + 18 x ^ { 7 } - 14 x ^ { 6 } - 3 x + 6 } { \left( x ^ { 7 } - 2 \right) ^ { 2 } }$

Question

Quizplus · Accepted Answer

To find the derivative of the function, we use the quotient rule. Let $u(x) = x^2-3x+2$ and $v(x) = x^7-2$. Then,
\begin{align*}
y' &= \frac{u'(x)v(x) - u(x)v'(x)}{[v(x)]^2} \
&= \frac{(2x-3)(x^7-2) - (x^2-3x+2)(7x^6)}{(x^7-2)^2} \
&= \frac{-5x^8 + 18x^7 - 14x^6 - 4x + 6}{(x^7-2)^2}.
\end{align*}
Therefore, the correct answer is (C).

Find the Derivative of the Function y=x2−3x+2x7−2y = \frac { x ^ { 2 } - 3 x + 2 } { x ^ { 7 } - 2 }y=x7−2x2−3x+2​

Find the Derivative of the Function $y = \frac { x ^ { 2 } - 3 x + 2 } { x ^ { 7 } - 2 }$