Step 1: Identify the function you need to differentiate, which is f(x) = 4x^2 + 3x - 5.
Step 2: Recall the power rule for differentiation: if f(x) = ax^n, then f'(x) = n * ax^(n-1).
Step 3: Differentiate the first term, 4x^2. Using the power rule, the derivative is 2 * 4 * x^(2-1) = 8x.
Step 4: Differentiate the second term, 3x. This is the same as 3x^1. Using the power rule, the derivative is 1 * 3 * x^(1-1) = 3.
Step 5: Differentiate the third term, -5. The derivative of a constant is 0.
Step 6: Combine the derivatives from Steps 3, 4, and 5. So, f'(x) = 8x + 3 + 0.
Step 7: Simplify the expression. The final result is f'(x) = 8x + 3.
Differentiation – The process of finding the derivative of a function, which represents the rate of change of the function with respect to its variable.
Power Rule – A basic rule in calculus used to differentiate functions of the form f(x) = ax^n, where the derivative is f'(x) = n * ax^(n-1).
