Question

differentiate.
y = ln (6x² - 7x + 5)
y = □

Explanation:

Step1: Apply the chain rule

Let \( u = 6x^{2}-7x + 5\), then \( y=\ln(u)\). The chain rule states that \(\frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx}\).
For \( y = \ln(u)\), \(\frac{dy}{du}=\frac{1}{u}\).
For \( u=6x^{2}-7x + 5\), \(\frac{du}{dx}=12x-7\).

Step2: Substitute \(u\) back

Substitute \(u = 6x^{2}-7x + 5\) into \(\frac{dy}{dx}=\frac{1}{u}\cdot(12x - 7)\).

Answer:

\(\frac{12x-7}{6x^{2}-7x + 5}\)