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The question asks to find the derivative \(\frac{dy}{dx}\) of the function:

\[
y = 3x^4 + \sin(2x) + \cos(3x)
\]

Let's differentiate each term with respect to \(x\):

1. \( \frac{d}{dx}(3x^4) = 12x^3 \)
2. \( \frac{d}{dx}(\sin(2x)) = 2\cos(2x) \) (using the chain rule, where the derivative of \(\sin(u)\) is \(\cos(u)\) and the derivative of \(2x\) is 2)
3. \( \frac{d}{dx}(\cos(3x)) = -3\sin(3x) \) (again, using the chain rule, where the derivative of \(\cos(u)\) is \(-\sin(u)\) and the derivative of \(3x\) is 3)

Now, combining these results, we get:

\[
\frac{dy}{dx} = 12x^3 + 2\cos(2x) - 3\sin(3x)
\]

Let me know if you'd like further clarification or details! Here are five related questions for practice:

1. What is the second derivative \(\frac{d^2y}{dx^2}\) for the same function?
2. How would the derivative change if the function included an exponential term like \(e^{x^2}\)?
3. Can you find the critical points of the function \(y = 3x^4 + \sin(2x) + \cos(3x)\)?
4. What is the integral of \(y = 3x^4 + \sin(2x) + \cos(3x)\)?
5. How do you apply the chain rule to differentiate more complex functions?

**Tip:** Always remember to apply the chain rule when differentiating composite functions!

Jika y = 3x^4 + sin(2x) + cos(3x), maka dy/dx = ...

Learn how to differentiate the function y = 3x^4 + sin(2x) + cos(3x) using the power rule and chain rule. This solution walks through each term and explains how to apply differentiation to trigonometric functions and composite functions.

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