Find the derivative for f(x)=-x^2+x
Do I put the -x^2 as a denominator? How would I solve it if that's what I'm supposed to do?
To find the derivative of f(x) = -x^2 + x, you need to apply the power rule for derivatives. The power rule states that if you have a term in the form of x^n, the derivative will be nx^(n-1).
Let's go step by step to find the derivative of f(x):
Step 1: Differentiate -x^2 term
The derivative of -x^2 is found by applying the power rule: -2x^(2-1) = -2x^1 = -2x.
Step 2: Differentiate x term
The derivative of x is found by applying the power rule: 1x^(1-1) = 1x^0 = 1.
Step 3: Combine the derivatives
Now, we have the derivatives of the individual terms: -2x and 1. To find the derivative of the entire function, simply combine these derivatives: -2x + 1.
Therefore, the derivative of f(x) = -x^2 + x is -2x + 1.
Note: There is no need to put -x^2 as a denominator when finding the derivative.