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Techniques of Differentiation - Derivatives of Natural Logarithmic Functions

Techniques of Differentiation - Derivatives of Natural Logarithmic Functions

TGM Original Questions

Evaluate each of the following.

  1. \(\frac{\mathrm{d}}{\mathrm{d}x}(\ln 6x^3)\)

  2. \(\frac{\mathrm{d}}{\mathrm{d}x}(\ln 4x^5)\)

  3. \(\frac{\mathrm{d}}{\mathrm{d}x}\left[\ln (4x^2 - 3)\right]\)

  4. \(\frac{\mathrm{d}}{\mathrm{d}x}\left[\ln (2x^2 - 5)\right]\)

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Answer:(i) \(\dfrac3x\) (ii) \(\dfrac5x\) (iii) \(\dfrac{8x}{4x^2-3}\) (iv) \(\dfrac{4x}{2x^2-5}\)

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