Chain Rule
Asked by Muhammad Iqbal · 1 year ago
Explain the chain rule and provide a simple example.
1 Answer
The chain rule is used to differentiate composite functions:
1. If y = f(u) and u = g(x), then dy/dx = (dy/du) * (du/dx)
2. In other words, multiply the derivative of the outer function by the derivative of the inner function
3. Example: y = (x² + 1)³
Let u = x² + 1, so y = u³
dy/du = 3u²
du/dx = 2x
dy/dx = 3u² * 2x = 3(x² + 1)² * 2x
4. The chain rule is essential for differentiating complex functions.
1. If y = f(u) and u = g(x), then dy/dx = (dy/du) * (du/dx)
2. In other words, multiply the derivative of the outer function by the derivative of the inner function
3. Example: y = (x² + 1)³
Let u = x² + 1, so y = u³
dy/du = 3u²
du/dx = 2x
dy/dx = 3u² * 2x = 3(x² + 1)² * 2x
4. The chain rule is essential for differentiating complex functions.
NEET Faculty · 1 year ago
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