Section 3.3: Derivative of Trigonometric Functions:

  1. Differentiate the following functions.   solution
  2. (i) \(y=3\sin(\theta) - 4e^{\theta}\, \tan (\theta) \)     (ii) \(y=\sec(\theta) (2\theta - 4 \cos(\theta)) \)   

  3.   Differentiate the following functions.   solution
  4. (i) \(f(x)=\dfrac{2x}{x-\cot x} \)     (ii) \(y= 5 t\cos t \tan t \)

  5. If   \( f(x) = e^x \sec x \), then find \( f'(0)\).    solution
  6. Differentiate:   (a) \( f(x)= x \cos x \)   solution     (b) \(\displaystyle{f(x)= \frac{\tan x}{x^2} }\),     solution
  7. If   \( f (\theta)= \theta \cos \theta \),  find the value of \( f'(0) \).     solution
  8.  If   \( f(\pi/3)= 4,   f'(\pi/3)=-2\)  and   \(g(x)=f(x) \sin x \), then find \( g'(\pi/3)\).    solution
  9. Find an equation of the tangent line to the curve  \(y= x-\cos x \)  at  \( x=0\).    solution
  10. Find an equation of the tangent line to the curve \(y=2\sec (x)-4 \cos (x)\) at the point \( \left(\frac{\pi}{3}, 2\right)\).   solution
  11. If   \( f(x) = \sec x \), then find \(f''(\pi/4)\).    solution
  12. Suppose \(f(\pi / 3)= 6\) and \(f'(\pi / 3)=-5,\) and let \(g(x)=f(x) \sin (x)\) and \(h(x)=\cos (x) / f(x) \). Find (a) \(g'(\pi/3) \) and (b) \(h'(\pi/3) \).
  13. solution

 

 

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