Learning Outcomes
 Find the derivatives of sine and cosine functions .
 Find the derivatives of the standard trigonometric functions.
 Calculate the higherorder derivatives of the sine and cosine functions.
Textbook
 Chapter 3.5 Derivatives of Trigonometric Functions
Textbook Assignment
 p. 285: 177, 179, 185, 187, 191195 odd
WeBWork Assignment
 DerivativesTrigonometric
Exit problems of the session

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