Find the derivatives of the functions in Exercises 1–42.


𝔂 = x⁵ - 0.125x² + 0.25x

Verified step by step guidance

1. Identify the function for which you need to find the derivative: \( y = x^5 - 0.125x^2 + 0.25x \).
2. Apply the power rule for differentiation, which states that the derivative of \( x^n \) is \( nx^{n-1} \).
3. Differentiate each term of the function separately: For \( x^5 \), the derivative is \( 5x^4 \).
4. For the term \(-0.125x^2\), apply the power rule to get \(-0.25x\).
5. For the term \(0.25x\), the derivative is simply \(0.25\), since the derivative of \(x\) is 1.