Find the derivative of the following function. $y = \ln \left( 4 x ^ { 3 } - 9 x \right) - 3 x$
A) $\frac { 12 x ^ { 2 } - 9 x } { x \left( 4 x ^ { 2 } - 9 \right) } - 3$
B) $\frac { 1 } { x \left( 4 x ^ { 2 } - 9 \right) } - 3$
C) $\frac { 12 x ^ { 2 } - 9 } { x \left( 4 x ^ { 2 } - 9 \right) } - 3$
D) $\frac { 12 x ^ { 2 } } { x \left( 4 x ^ { 2 } - 9 \right) } - 3$
E) $\frac { 1 } { x \left( 4 x ^ { 2 } - 1 \right) } - 3$

Question

Quizplus · Accepted Answer

The derivative of $y = \ln(4x^3 - 9x) - 3x$ is found using the chain rule for the logarithmic part and the power rule for the linear part. The derivative of $\ln(u)$ is $\frac{1}{u} \cdot \frac{du}{dx}$, where $u = 4x^3 - 9x$. Thus, $\frac{du}{dx} = 12x^2 - 9$. The derivative of $-3x$ is $-3$. Combining these, the derivative is $\frac{12x^2 - 9}{4x^3 - 9x} - 3$, which simplifies to $\frac{12x^2 - 9}{x(4x^2 - 9)} - 3$.

Find the Derivative of the Following Function y=ln⁡(4x3−9x)−3xy = \ln \left( 4 x ^ { 3 } - 9 x \right) - 3 xy=ln(4x3−9x)−3x

Find the Derivative of the Following Function $y = \ln \left( 4 x ^ { 3 } - 9 x \right) - 3 x$