Find the derivative of f(x) = x3 - 3x2+2x - 5 with respect to x.
Get the complete, step-by-step math solution for: "Find the derivative of f(x) = x³ - 3x² + 2x - 5 with respect to x.". Powered by SolveForX AI math tutor.
Step-by-Step Solution
Step 1: Recall the Power Rule and Sum/Difference Rule
To find the derivative of a polynomial function, we use several basic differentiation rules. The power rule states that the derivative of xn is nxn−1. The constant multiple rule allows us to pull constants out of the derivative, and the sum/difference rule lets us differentiate each term separately. The derivative of a constant is always zero.
Step 2: Apply the rules to each term
We apply the sum and difference rules to break down the derivative of the entire function into the derivatives of its individual terms. This allows us to handle each part of the polynomial separately.
Step 3: Differentiate each term
Now, we differentiate each term using the power rule and the constant multiple rule. For x3, the derivative is 3x2. For 3x2, it's 3⋅2x=6x. For 2x, it's 2⋅1=2. And for the constant term −5, its derivative is 0.
Step 4: Combine the derivatives
Finally, we combine the derivatives of all the individual terms to get the derivative of the original function f(x). This gives us the final expression for f'(x).