Final answer:
The derivative of the function f(x) = x³ + 2x is obtained by differentiating each term separately using the power rule, resulting in 3x² + 2.
Step-by-step explanation:
To find the derivative of the function f(x) = x³ + 2x, we will use basic differentiation rules. The derivative of a function gives us the rate at which the function's value is changing at any given point. For polynomials, each term is differentiated separately according to the power rule.
Steps to Differentiate f(x) = x³ + 2x:
- Differentiate the term x³: the power rule states that d/dx of xⁿ = n*xⁿ⁻¹, where n is the power. Thus, the derivative of x³ is 3*x².
- Differentiate the term 2x, which is a linear term and has the derivative of the coefficient, 2.
- Add the derivatives of the individual terms to get the overall derivative of f(x), which is 3x² + 2.
Therefore, the derivative of f(x) = x³ + 2x is 3x² + 2.