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Find the derivative of f(x) = 5x^2 + 3x - 1. (2020)
Find the derivative of f(x) = 5x^2 + 3x - 1. (2020)
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Practice Questions
1 question
Q1
Find the derivative of f(x) = 5x^2 + 3x - 1. (2020)
10x + 3
5x + 3
10x - 1
5x^2 + 3
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Using the power rule, f'(x) = 10x + 3.
Questions & Step-by-step Solutions
1 item
Q
Q: Find the derivative of f(x) = 5x^2 + 3x - 1. (2020)
Solution:
Using the power rule, f'(x) = 10x + 3.
Steps: 7
Show Steps
Step 1: Identify the function you want to differentiate, which is f(x) = 5x^2 + 3x - 1.
Step 2: Recall the power rule for derivatives. The power rule states that if you have a term in the form of ax^n, the derivative is n * ax^(n-1).
Step 3: Apply the power rule to the first term, 5x^2. Here, a = 5 and n = 2. The derivative is 2 * 5 * x^(2-1) = 10x.
Step 4: Apply the power rule to the second term, 3x. Here, a = 3 and n = 1. The derivative is 1 * 3 * x^(1-1) = 3.
Step 5: The third term is a constant (-1). The derivative of a constant is 0.
Step 6: Combine the derivatives from Steps 3, 4, and 5. So, f'(x) = 10x + 3 + 0.
Step 7: Simplify the expression. The final derivative is f'(x) = 10x + 3.
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