23–51. Calculating derivatives Find the derivative of the following functions. y = tan x + cot x
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Step 1: Identify the functions involved in the expression. The given function is . Here, and are trigonometric functions.
Step 2: Recall the derivatives of the basic trigonometric functions. The derivative of is , and the derivative of is .
Step 3: Apply the sum rule for derivatives. The sum rule states that the derivative of a sum of functions is the sum of their derivatives. Therefore, .
Step 4: Substitute the derivatives of the individual functions into the expression. This gives .
Step 5: Simplify the expression if possible. In this case, the expression is already in its simplest form.
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