Find the derivative of the function.
$$f ( x ) = \left( x ^ { 2 } + 1 \right) \left( \frac { 9 x - 1 } { 7 x + 1 } \right)$$
A) $\frac { 63 x ^ { 3 } + 135 x ^ { 2 } + 49 x + 9 } { 7 ( 7 x + 1 ) ^ { 2 } }$
B) $\frac { 63 x ^ { 3 } + 135 x ^ { 2 } + 49 x + 9 } { 7 ( 7 x + 1 ) }$
C) $\frac { 126 x ^ { 3 } + 20 x ^ { 2 } - 2 x + 16 } { ( 7 x + 1 ) ^ { 2 } }$
D) $\frac { 126 x ^ { 3 } + 20 x ^ { 2 } - 2 x + 16 } { ( 7 x + 1 ) }$

Question

Quizplus · Accepted Answer

To find the derivative of the given function, we can use the product rule and the quotient rule of differentiation. Applying the product rule,
$$\frac{d}{dx}\left((x^2+1)\left(\frac{9x-1}{7x+1}\right)\right) = \frac{d}{dx}(x^2+1)\cdot\left(\frac{9x-1}{7x+1}\right)+(x^2+1)\cdot\frac{d}{dx}\left(\frac{9x-1}{7x+1}\right)$$
$$=2x\cdot\frac{9x-1}{7x+1}+(x^2+1)\cdot\frac{(9(7x+1))-(7(9x-1))}{(7x+1)^2}$$
$$=\frac{126x^3+20x^2-2x+16}{(7x+1)^2}$$
Therefore, the correct choice is C.

Find the Derivative of the Function f(x)=(x2+1)(9x−17x+1)f ( x ) = \left( x ^ { 2 } + 1 \right) \left( \frac { 9 x - 1 } { 7 x + 1 } \right)f(x)=(x2+1)(7x+19x−1​)

Find the Derivative of the Function $f ( x ) = \left( x ^ { 2 } + 1 \right) \left( \frac { 9 x - 1 } { 7 x + 1 } \right)$