Learn how to find the derivative of x^2 + x. The derivative is d/dx[x^2 + x].
Below is the graph of f(x) = x^2 + 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 need to recognize that x^2 and x are both monomials, each of which can be differentiated using the Power Rule.
💡 Why this works: The Power Rule is applied to each term separately: x^2 and x. Since these terms are powers of x, we will differentiate them using the Power Rule to find the rate of change of the function at any point.
We differentiate each term using the Power Rule: d/dx[x^2] = 2x and d/dx[x] = 1.
💡 Why this works: The Power Rule tells us to multiply the exponent of x by the coefficient and reduce the exponent by 1. For x^2, the derivative is 2x, and for x, the derivative is 1, giving us the final result of f'(x) = 2x + 1.
Now, we combine the results of the individual derivatives: 2x + 1.
💡 Why this works: After applying the Power Rule to each term, we arrive at f'(x) = 2x + 1. This is the simplified form of the derivative, showing how the function x^2 + x changes at any given value of 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.
Calculate any derivative instantly with step-by-step solutions. Perfect for students, teachers, and anyone learning calculus.