Questions: Find dy/dx. y=4(tan x+sec x)(tan x-sec x) dy/dx=□

Transcript text: Find $\frac{d y}{d x}$. \[ \begin{array}{l} y=4(\tan x+\sec x)(\tan x-\sec x) \\ \frac{d y}{d x}=\square \end{array} \]

Solution

Solution Steps

To find $\frac{d y}{d x}$ for the given function $y = 4(\tan x + \sec x)(\tan x - \sec x)$, we can use the product rule and the chain rule. First, expand the expression inside the parentheses to simplify the differentiation process. Then, differentiate the resulting expression with respect to $x$.

Step 1: Define the Function

We start with the function given by \[ y = 4(\tan x + \sec x)(\tan x - \sec x). \]

Step 2: Simplify the Expression

Upon simplifying the expression, we find that \[ y = -4. \]

Step 3: Differentiate the Function

Next, we differentiate $y$ with respect to $x$: \[ \frac{d y}{d x} = 0. \]