Learn how to find the derivative of x + 1. The derivative is d/dx[x + 1].
Below is the graph of f(x) = x + 1 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.
In the function x + 1, the term x is a linear function, and 1 is a constant. Since the Power Rule applies to terms of the form x^n, we need to apply it to the x term.
💡 Why this works: The Power Rule tells us that the derivative of x^n is n*x^(n-1). The term 1 is a constant and its derivative is zero. Therefore, we focus on differentiating x, which follows the Power Rule.
We apply the Power Rule to x. The derivative of x^1 is simply 1. Since the derivative of the constant 1 is 0, we add these results.
💡 Why this works: Applying the Power Rule to the x term gives us 1. The derivative of the constant 1 is 0, so the final result is simply 1.
After applying the rules, we see that the derivative of x + 1 is simply 1.
💡 Why this works: The derivative is correct because we followed the rules for differentiating a linear function and a constant. The derivative of a linear function like x + 1 is always constant, and in this case, it's equal to 1.
[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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