Learn how to find the derivative of x^2 + tan x. The derivative is d/dx[x^2 + tan x].
Below is the graph of f(x) = x^2 + 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.
We recognize that x^2 and tan x are separate terms. The term x^2 fits the structure of the Power Rule, while tan x requires the use of standard trigonometric differentiation rules.
💡 Why this works: The Power Rule applies to x^2, as it involves a power of x, and tan x needs to be differentiated using its known derivative.
First, differentiate x^2 using the Power Rule: d/dx[x^2] = 2x. Then, differentiate tan x using the standard rule for the derivative of tangent: d/dx[tan x] = sec^2(x).
💡 Why this works: By applying these rules, we obtain the derivative of f(x) = x^2 + tan x, which is f'(x) = 2x + sec^2(x).
The derivative simplifies to 2x + sec^2(x), which is the final form. This derivative is now fully simplified and ready for use.
💡 Why this works: After applying the rules and simplifying, we verify that the derivative is correct, with no further simplifications needed.
[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.