Given the function $y = x^3 - \frac{10}{x^4}$, we need to find the derivative $\frac{dy}{dx}$.

Step 1: Differentiate $y = x^3$

Using the power rule $\frac{d}{dx}(x^n) = nx^{n-1}$, we have:

$\frac{d}{dx}(x^3) = 3x^2$

Step 2: Differentiate $-\frac{10}{x^4}$

Rewrite $-\frac{10}{x^4}$ as $-10x^{-4}$, then apply the power rule:

$\frac{d}{dx}(-10x^{-4}) = -10 \cdot (-4) x^{-5} = 40x^{-5}$

Step 3: Combine the results

Now, combining the derivatives:

$\frac{dy}{dx} = 3x^2 + 40x^{-5}$

Alternatively, this can be written as:

$\frac{dy}{dx} = 3x^2 + \frac{40}{x^5}$

That is the derivative of $y = x^3 - \frac{10}{x^4}$.

Do you want more details or have any questions?

Here are 5 related questions to explore:

1. How do we apply the chain rule in differentiation?
2. What is the derivative of a product of two functions?
3. How do we find the second derivative of this function?
4. How do you differentiate an implicit function?
5. How do we apply the quotient rule in differentiation?

Tip: Always simplify the function as much as possible before differentiating to make the process easier.