Learning Outcomes

  1. Find the derivatives of sine and cosine functions .
  2. Find the derivatives of the standard trigonometric functions.
  3. Calculate the higher-order derivatives of the sine and cosine functions.

Textbook

  • Chapter 3.5   Derivatives of Trigonometric Functions  

Textbook Assignment

  • p. 285:    177, 179, 185, 187, 191-195 odd

WeBWork Assignment

  • Derivatives-Trigonometric

Exit problems of the session 

  1. Find the derivative of the following functions:

    (a).  $f(x)=3\tan x+\dfrac{5}{x}$    (b).   $g(x)=2\sin x\cos x$   (c).  $h(x)=\dfrac{\sin x}{1-\cos x}$
  2. Find the second order derivative $y”$ for the given function $y=\csc x$.

 

Key Concepts

  • Derivative of sine function:    $\dfrac{d}{dx}(\sin x)=\cos x$
  • Derivative of cosine function:   $\dfrac{d}{dx}(\cos x)=-\sin x$
  • Derivative of tangent function:   $\dfrac{d}{dx}(\tan x)=\sec^2 x$
  • Derivative of cotangent function:   $\dfrac{d}{dx}(\cot x)=-\csc^2 x$
  • Derivative of secant function:   $\dfrac{d}{dx}(\sec x)=\tan x\sec x$
  • Derivative of cosecant function:   $\dfrac{d}{dx}(\csc x)=-\cot x\csc x$

 

Videos and Practice Problems of Selected Topics

  1. $\rhd$ Derivatives of $\sin(x)$ and $\cos(x)$. (3:40)
  2. $\rhd$ Worked Examples: derivatives of $\sin(x)$ and $\cos(x)$. (5:13) Find the derivative of $g(x)=7\sin(x)-3\cos(x)-\left(\dfrac{\pi}{\sqrt[3]{x}}\right)^2$.
  3. * Practice: Derivatives of $\sin(x)$ and $\cos(x)$. (4 problems)
  4. $\rhd$ Derivatives of $\tan(x)$ and $\cot(x)$ (4:37) Use the quotient rule to derive formulas for the derivative of $\tan(x)$ and $\cot(x)$.
  5. $\rhd$ Derivatives of $\sec(x)$ and $\csc(x)$ (4:27) Use the quotient rule to derive formulas for the derivative of $\sec(x)$ and $\csc(x)$.
  6. $\rhd$ Product rule (8:03) Find the derivative of $h(x) = (x^2)(x^3+4)$ (first 3:20 minutes) and $y= (\sin x)(\cos x) (x^2+1)$.
  7. $\rhd$ Quotient rule (7:37) Find the derivative of $y=\dfrac{x^2+1}{x^5+x}$ (first 3:34 minues) and $y=\dfrac{\tan x}{x^{3/2}+5x}$.