Sure, let's differentiate another function. Please provide the function you would like to differentiate, or if you'd like to see another example, I can provide one.

For now, here's another example for practice:

Differentiate $g(x) = \frac{2x^3 - 3x + 1}{x^2}$.

To differentiate $g(x)$, we can use the quotient rule, which states that if $g(x) = \frac{u(x)}{v(x)}$, then the derivative $g'(x)$ is given by:

$g'(x) = \frac{u'(x)v(x) - u(x)v'(x)}{(v(x))^2}$

Here, let $u(x) = 2x^3 - 3x + 1$ and $v(x) = x^2$.

First, we find the derivatives of $u(x)$ and $v(x)$:

1. $u(x) = 2x^3 - 3x + 1$ $u'(x) = \frac{d}{dx}(2x^3 - 3x + 1) = 6x^2 - 3$

2. $v(x) = x^2$ $v'(x) = \frac{d}{dx}x^2 = 2x$

Now, apply the quotient rule:

$g'(x) = \frac{(6x^2 - 3)x^2 - (2x^3 - 3x + 1)2x}{(x^2)^2}$

Simplify the numerator:

$g'(x) = \frac{(6x^4 - 3x^2) - (4x^4 - 6x^2 + 2x)}{x^4}$

Distribute and combine like terms:

$g'(x) = \frac{6x^4 - 3x^2 - 4x^4 + 6x^2 - 2x}{x^4}$ $g'(x) = \frac{2x^4 + 3x^2 - 2x}{x^4}$

Separate the terms:

$g'(x) = \frac{2x^4}{x^4} + \frac{3x^2}{x^4} - \frac{2x}{x^4}$ $g'(x) = 2 + \frac{3}{x^2} - \frac{2}{x^3}$

Thus, the derivative of $g(x) = \frac{2x^3 - 3x + 1}{x^2}$ is:

$g'(x) = 2 + \frac{3}{x^2} - \frac{2}{x^3}$

Do you want details or have any questions?

Here are 8 related questions to expand your understanding:

1. How do you find the derivative of a function using the power rule?
2. What is the product rule in differentiation, and how is it applied?
3. How do you find the derivative of a function using the chain rule?
4. How do you find the second derivative of a function?
5. What is implicit differentiation and when is it used?
6. How do you differentiate logarithmic functions?
7. How do you find the derivative of a function using the logarithmic differentiation?
8. What are parametric equations and how do you find their derivatives?

Tip: When using the quotient rule, make sure to simplify the numerator as much as possible before dividing by the square of the denominator.