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Easy: Powers of a linear expression
For a function inside another, f(g(x)), the derivative is f′(g(x))·g′(x): differentiate the outside, leaving the inside alone, then multiply by the derivative of the inside. For a power of an expression, (u)ⁿ becomes n(u)ⁿ⁻¹·u′.
Find the derivative.
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When a function is applied to something other than plain x, such as (3x + 1)⁵ or √(2x + 5). Differentiate the outside, keep the inside, then multiply by the derivative of the inside.
5(3x + 1)⁴ × 3 = 15(3x + 1)⁴. Forgetting the × 3 from the inside is the most common chain rule mistake.
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