The rules of differentiation
Try the power, product, quotient and chain rules on a number at one point, and check them against tangents and normals on a graph.
- UK: Year 12
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- Iran: grade 12
- Afghanistan: grade 12
- Syria: grade 11
- Palestine: grade 12
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- Russia: grade 10
Guide
Power rule: (xn)′ = nxn − 1. The gradient of the tangent at a point is the derivative there. The normal is perpendicular to the tangent, so its gradient is −1f′.
Product rule: (u·v)′ = u′v + uv′. Quotient rule: (uv)′ = u′v − uv′v2. The derivative of a product is not the product of the derivatives.
Chain rule: (f(g(x)))′ = f′(g(x))·g′(x). First the derivative of the "outside" with the inside left alone, then multiply by the derivative of the "inside".