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The given function is \( f(x, y) = 5x^4 - y^2 \), and the question asks for the partial derivative of \( f \) with respect to \( x \).

### Steps for calculating the partial derivative of \( f(x, y) \) with respect to \( x \):
- Treat \( y \) as a constant because we are differentiating with respect to \( x \).
- Differentiate \( 5x^4 \) with respect to \( x \), and the derivative of \( y^2 \) with respect to \( x \) will be zero since \( y \) is treated as a constant.

1. The derivative of \( 5x^4 \) with respect to \( x \) is:
   \[
   \frac{\partial}{\partial x}(5x^4) = 20x^3
   \]

2. The derivative of \( -y^2 \) with respect to \( x \) is:
   \[
   \frac{\partial}{\partial x}(-y^2) = 0
   \]

### Therefore, the partial derivative of \( f(x, y) \) with respect to \( x \) is:
\[
\frac{\partial f}{\partial x} = 20x^3
\]

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Here are five related questions:
1. What is the partial derivative of \( f(x, y) = 5x^4 - y^2 \) with respect to \( y \)?
2. How does the chain rule apply to partial derivatives?
3. Can you find the second partial derivative of \( f(x, y) \) with respect to \( x \)?
4. How do you calculate the gradient of a function involving multiple variables?
5. What is the geometrical interpretation of a partial derivative?

**Tip:** In multivariable calculus, partial derivatives measure how a function changes as one variable changes while keeping the others constant.

Jika diketahui bahwa f(x,y) = 5x^4 - y^2 maka turunan parsial terhadap x yang tepat adalah

Learn how to compute the partial derivative of the function f(x, y) = 5x^4 - y^2 with respect to x. This problem involves concepts from multivariable calculus, including the application of partial derivatives.

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