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Techniques of Differentiation - Derivatives of Trigonometric Functions

Techniques of Differentiation - Derivatives of Trigonometric Functions

Differentiate the following with respect to \(x\) and simplify your answers.

  1. \(e^x \cos^2 x\)
  2. \(\cos^{-1} 3x\)
  3. \(7^{\ln x}\)
  4. \(\ln \left( \frac{1 + e^{3x}}{1 - e^{3x}} \right)\)

Solution:

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Answer:(a) \(e^x\cos x(\cos x-2\sin x)\). (b) \(-\frac3{\sqrt{1-9x^2}}\), for \(|x|<\frac13\). (c) \(\frac{7^{\ln x}\ln7}{x}\), for \(x>0\). (d) \(\frac{6e^{3x}}{1-e^{6x}}\), for \(x<0\).

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