$\text { Differentiate the function } f ( x ) = \ln \left( 8 x ^ { 2 } - 4 x + 11 \right) \text {. }$
A)$\frac { 16 x - 4 } { \left( 8 x ^ { 2 } - 4 x + 11 \right) ^ { 2 } }$
B) $\frac { 16 x } { 8 x ^ { 2 } - 4 x + 11 }$
C) $\frac { 16 x + 4 } { 8 x ^ { 2 } - 4 x + 11 }$
D) $\frac { 16 x - 4 } { 8 x ^ { 2 } - 4 x + 11 }$
E) $\frac { 1 } { 8 x ^ { 2 } - 4 x + 11 }$

Question

$\text { Differentiate the function } f ( x ) = \ln \left( 8 x ^ { 2 } - 4 x + 11 \right) \text {. }$ 
A)$\frac { 16 x - 4 } { \left( 8 x ^ { 2 } - 4 x + 11 \right) ^ { 2 } }$
B) $\frac { 16 x } { 8 x ^ { 2 } - 4 x + 11 }$
C) $\frac { 16 x + 4 } { 8 x ^ { 2 } - 4 x + 11 }$
D) $\frac { 16 x - 4 } { 8 x ^ { 2 } - 4 x + 11 }$
E) $\frac { 1 } { 8 x ^ { 2 } - 4 x + 11 }$

Quizplus · Accepted Answer

Using the chain rule, we have

$$\frac{d}{dx} \ln \left( 8 x ^ { 2 } - 4 x + 11 \right) = \frac{1}{8x^2-4x+11} \cdot \frac{d}{dx} (8x^2-4x+11)$$

Simplifying the derivative of the inside function, we have

$$\frac{d}{dx} (8x^2-4x+11) = 16x-4$$

Substituting back into the original expression, we have

$$\frac{d}{dx} \ln \left( 8 x ^ { 2 } - 4 x + 11 \right) = \frac{16x-4}{8x^2-4x+11}$$

Therefore, the answer is (D).

Differentiate the function f(x)=ln⁡(8x2−4x+11). \text { Differentiate the function } f ( x ) = \ln \left( 8 x ^ { 2 } - 4 x + 11 \right) \text {. } Differentiate the function f(x)=ln(8x2−4x+11).

$\text { Differentiate the function } f ( x ) = \ln \left( 8 x ^ { 2 } - 4 x + 11 \right) \text {. }$