what is the derivative of 3x-1/2x^2-6
To find the derivative of the function f(x) = 3x - 1/2x^2 - 6, you can apply the power rule and the constant rule for differentiation.
1. Start by identifying the terms in your function: f(x) = 3x - (1/2)x^2 - 6. The terms are 3x, (1/2)x^2, and 6.
2. For each term, use the power rule to differentiate. The power rule states that the derivative of x^n is nx^(n-1).
- The first term 3x has a power of 1. Applying the power rule, the derivative is 3 * 1x^(1-1) = 3(1) = 3.
- The second term (1/2)x^2 has a power of 2. Applying the power rule, the derivative is (1/2) * 2x^(2-1) = x.
- The third term 6 is a constant, and the derivative of a constant is always 0.
3. Combine the derivatives of each term to find the overall derivative of the function:
f'(x) = derivative of 3x - derivative of (1/2)x^2 - derivative of 6
= 3 - x - 0
= 3 - x
Therefore, the derivative of the function f(x) = 3x - 1/2x^2 - 6 is f'(x) = 3 - x.