Opgave 1: Bestem f'(x) når: f(x)=1/4 x^4-2x

For at bestemme den afledte funktion \( f'(x) \) af funktionen \( f(x) = \frac{1}{4}x^4 - 2x \), anvender vi regnereglerne for differentiation.

Funktionen \( f(x) = \frac{1}{4}x^4 - 2x \) består af to led, og vi kan differentiere hvert led for sig:

1. For det første led \( \frac{1}{4}x^4 \), anvender vi potensreglen, som siger at hvis \( f(x) = ax^n \), så er \( f'(x) = n \cdot ax^{n-1} \). Her er \( a = \frac{1}{4} \) og \( n = 4 \), så:

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Explore the differentiation of the polynomial function f(x) = 1/4 x^4 - 2x using the power rule. This step-by-step solution is suitable for students in Grades 11-12 who are learning about calculus and differentiation.

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