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Chapter 3: Problem 33

Find the derivative of the following functions. $$y=\sec x+\csc x$$

Short Answer

Expert verified
Answer: The derivative of the function $$y = \sec x + \csc x$$ is $$\frac{dy}{dx} = \sec x \tan x - \csc x \cot x$$.

Step by step solution

01

Differentiate sec(x)

Recall the derivative of sec(x) with respect to x: $$\frac{d}{dx}(\sec x) = \sec x \tan x$$ Step 2: Differentiate csc(x)
02

Differentiate csc(x)

Recall the derivative of csc(x) with respect to x: $$\frac{d}{dx}(\csc x) = -\csc x \cot x$$ Step 3: Add the individual derivatives
03

Combine the derivatives

Now, we just add the derivatives found in steps 1 and 2 to find the derivative of the entire function: $$\frac{d}{dx}(y) = \frac{d}{dx}(\sec x + \csc x) = \sec x \tan x - \csc x \cot x$$ So, the derivative of the function $$y = \sec x + \csc x$$ is: $$\frac{dy}{dx} = \sec x \tan x - \csc x \cot x$$

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