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📐 Mathematics  ·  Limits and Derivatives  ·  JEE

Find d/dx [f(g(x))] when f(u) = u² and g(x) = sin x.

Answer: 2sin x cos x.

  • A 2sin x cos x
  • B sin²x
  • C 2 sin x
  • D cos²x

Correct answer: A. 2sin x cos x

Explanation: Chain rule: f'(g(x))×g'(x) = 2sin(x) × cos(x) = 2sinx cosx = sin 2x.

xyP (a, f(a))Q (b, f(b))secant PQtangent at PAs Q slides toward P, secant approaches tangent

As point Q slides along the curve toward P, the secant line PQ rotates into the tangent line at P, whose slope is the derivative.

Concept context

Rate of change, differentiation rules, and applications

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