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Over 1 month ago
Prompt Details
Model
Chat - GPT-3.5 (gpt-3.5-turbo)
Token size
180 ($0.00040 / call)
Example input
Math problem: Find the derivative of f(x) = x^2 + 3x - 2
Example output
Step 1: Use the power rule of differentiation, which says that the derivative of x^n equals n*x^(n-1). Applying this rule to each term in f(x), we get:
f'(x) = 2x + 3
Step 2: Double-check the derivative by using the definition of the derivative, which is the limit of the difference quotient f(x + h) - f(x) / h as h goes to 0. We have:
[f(x + h) - f(x)] / h = [(x + h)^2 + 3(x + h) - 2 - (x^2 + 3x - 2)] / h
= (2xh + h^2 + 3h) / h
= 2x + h + 3
Taking the limit as h approaches 0, we get:
lim h->0 [(2xh + h^2 + 3h) / h] = 2x + 3
This matches the derivative we found in step 1, so we can be confident in our answer.
Solution: f'(x) = 2x + 3.