Differentiate the function.

*y* = 

7

*x*

 + 3*x*

6*x*2

We are tasked with differentiating the function:

\[
y = \frac{7x + 3x}{6x^2}
\]

### Step 1: Simplify the function
First, combine like terms in the numerator:

\[
y = \frac{7x + 3x}{6x^2} = \frac{10x}{6x^2}
\]

Now, simplify the fraction:

\[
y = \frac{10}{6x} = \frac{5}{3x}
\]

### Step 2: Differentiate the simplified function
The function is now \( y = \frac{5}{3x} \), which can be rewritten as \( y = \frac{5}{3} \cdot x^{-1} \).

Now differentiate it with respect to \( x \):

\[
\frac{dy}{dx} = \frac{5}{3} \cdot \frac{d}{dx}(x^{-1}) = \frac{5}{3} \cdot (-1) x^{-2}
\]

Thus, the derivative is:

\[
\frac{dy}{dx} = -\frac{5}{3x^2}
\]

---

Would you

Differentiate the function: y = 7x + 3x / 6x^2

This problem demonstrates how to differentiate the function y = (7x + 3x) / 6x^2, using simplification techniques and the power rule. The solution walks through combining terms and applying differentiation step-by-step, making it suitable for high school calculus students (Grades 10-12).

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