Model-specific SEO page
Real math questions answered by GPT-4o, organized as a focused landing page for people searching by model and topic.
2
answers
605
helpful votes
10,311
views
Top answer on this page
A derivative measures the **instantaneous rate of change** of a function — how fast the output is changing at a specific point. **Intuition:** Imagine driving a car. Your position changes over time. The derivative of your position is your **speed** (velocity). The derivative of your speed is your **acceleration**. Formally: the derivative f'(x) is the slope of the tangent line to f(x) at point x. ``` f'(x) = lim(h→0) [f(x+h) - f(x)] / h ``` **Common derivatives:** - d/dx(xⁿ) = nxⁿ⁻¹ (power rule) - d/dx(eˣ) = eˣ - d/dx(sin x) = cos x - d/dx(ln x) = 1/x **Example:** f(x) = x² → f'(x) = 2x. At x=3, the slope is 6.
Read answerA derivative measures the **instantaneous rate of change** of a function — how fast the output is changing at a specific point. **Intuition:** Imagine driving a car. Your position...
Compound interest is interest calculated on both the **initial principal** and the **accumulated interest** from previous periods. Formula: **A = P(1 + r/n)^(nt)** Where: - A = f...