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.
The function f(x) = x + tan x is a sum of two terms: a linear term x and a trigonometric term tan x. The Power Rule applies to the linear term, while the derivative of tan x is handled using standard trigonometric differentiation rules.
💡 Why this works: We break the function into its components. For x, we apply the Power Rule, and for tan x, we use the known derivative of the tangent function, which is sec^2(x).
We apply the Power Rule to the term x and differentiate tan x using the standard rule. The Power Rule tells us that the derivative of x is 1. The derivative of tan x is sec^2(x).
💡 Why this works: The result of differentiating f(x) = x + tan x is f'(x) = 1 + sec^2(x).
The derivative f'(x) = 1 + sec^2(x) is already in its simplest form, as there are no like terms to combine.
💡 Why this works: This final expression is the correct derivative because it accurately reflects the differentiation of both the linear and trigonometric parts of the function.
[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.
Calculate any derivative instantly with step-by-step solutions. Perfect for students, teachers, and anyone learning calculus.