Find the derivative of f(x) = 5x^3 - 4x + 7. (2019)
Practice Questions
1 question
Q1
Find the derivative of f(x) = 5x^3 - 4x + 7. (2019)
15x^2 - 4
15x^2 + 4
5x^2 - 4
5x^2 + 4
Using the power rule, f'(x) = 15x^2 - 4.
Questions & Step-by-step Solutions
1 item
Q
Q: Find the derivative of f(x) = 5x^3 - 4x + 7. (2019)
Solution: Using the power rule, f'(x) = 15x^2 - 4.
Steps: 7
Step 1: Identify the function you want to differentiate, which is f(x) = 5x^3 - 4x + 7.
Step 2: Recall the power rule for differentiation. The power rule states that if you have a term in the form of ax^n, the derivative is a * n * x^(n-1).
Step 3: Apply the power rule to the first term, 5x^3. Here, a = 5 and n = 3. The derivative is 5 * 3 * x^(3-1) = 15x^2.
Step 4: Apply the power rule to the second term, -4x. Here, a = -4 and n = 1. The derivative is -4 * 1 * x^(1-1) = -4.
Step 5: The third term is a constant (7). The derivative of a constant is 0.
Step 6: Combine all the derivatives from the previous steps. The derivative f'(x) = 15x^2 - 4 + 0.
Step 7: Simplify the expression. The final result is f'(x) = 15x^2 - 4.
