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KCET2008MathematicsDifferentiation

If f (x⁵ )=5 x³ , then f^ (x) is equal to

Options

  1. A3 [5] x ²
  2. B3 [5] x
  3. C3 x
  4. D[5] x

Correct answer

A. 3 [5] x ²

Step-by-step solution

Given, f ( x ⁵ )=5 x ³ Let x ⁵= y x ³= y ^ 3 / 5 f ( y )=5 y ^ 3 / 5 or f ( x )=5 x ^ 3 / 5 On differentiating w.r.t. x, we get aligned f^ (x) &=5 3 5 x⁻² &= 3 [5] x² aligned

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