Learn how to find the derivative of x tan x. The derivative is d/dx[x tan x].
Below is the graph of f(x) = x tan x and its derivative f'(x). Notice how the original function and derivative relate to each other.
Original Function:
Derivative:
This derivative represents the rate of change of the original function. The calculation follows standard differentiation rules as shown in the step-by-step solution below.
x tan x is a product of a linear function (x) and a trigonometric function (tan x), which is why the Power Rule applies.
💡 Why this works: The Power Rule is used because the term x is treated as a power function of x, while tan x is differentiated using standard trigonometric rules. This structure suggests that the product rule is not needed, as the term x itself is simply treated as a first-degree term.
Differentiate each part of x tan x using the Power Rule. The derivative of x is 1, and the derivative of tan x is sec² x.
💡 Why this works: By applying the Power Rule to the x term and the derivative of tan x, we obtain the derivative of x tan x as f'(x) = tan x + x sec² x.
Simplify the expression and confirm that the result matches the expected derivative of x tan x.
💡 Why this works: The derivative of x tan x is d/dx[x tan x] = tan x + x sec² x. This result is verified through the proper application of the Power Rule and differentiation of tan x.
[Teaching explanation - to be filled]
[Application to this function - to be filled]
❌ Common Mistake:
Not simplifying the final answer
✅ Correct Approach:
Always simplify your derivative to its most reduced form
Double-check your work by comparing your steps with our solution. Use our calculator to verify each step of the differentiation process.
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