$\text { Find the derivative of the function } f ( x ) = \frac { x ^ { 5 } - 9 } { x ^ { 4 } } \text {. }$
A) $f ^ { t } ( x ) = 1 + \frac { 36 } { x ^ { 5 } }$
B) $f ^ { t } ( x ) = 1 - \frac { 36 } { x ^ { 5 } }$
C) $f ^ { t} ( x ) = 1 + \frac { 4 } { x ^ { 5 } }$
D) $f ^ { t } ( x ) = 1 - \frac { 9 } { x ^ { 5 } }$
E) $f ^ {t } ( x ) = 1 + \frac { 9 } { x ^ { 5 } }$

Question

$\text { Find the derivative of the function } f ( x ) = \frac { x ^ { 5 } - 9 } { x ^ { 4 } } \text {. }$ 
A) $f ^ { t } ( x ) = 1 + \frac { 36 } { x ^ { 5 } }$
B) $f ^ { t } ( x ) = 1 - \frac { 36 } { x ^ { 5 } }$
C) $f ^ { t} ( x ) = 1 + \frac { 4 } { x ^ { 5 } }$
D) $f ^ { t } ( x ) = 1 - \frac { 9 } { x ^ { 5 } }$
E) $f ^ {t } ( x ) = 1 + \frac { 9 } { x ^ { 5 } }$

Quizplus · Accepted Answer

Using the quotient rule, we have:$$f'(x) = \frac{(x^4)(5x^4) - (x^5 - 9)(4x^3)}{(x^4)^2} = \frac{5x^8 - 4x^8 + 36x^3}{x^8} = 1 + \frac{36}{x^5}$$

Find the derivative of the function f(x)=x5−9x4. \text { Find the derivative of the function } f ( x ) = \frac { x ^ { 5 } - 9 } { x ^ { 4 } } \text {. } Find the derivative of the function f(x)=x4x5−9​.

$\text { Find the derivative of the function } f ( x ) = \frac { x ^ { 5 } - 9 } { x ^ { 4 } } \text {. }$