Learn how to find the derivative of x + sin x. The derivative is d/dx[x + sin x].
Below is the graph of f(x) = x + sin 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 x + sin x consists of two parts: x and sin x. The Power Rule applies to the x term, and the derivative of sin x is handled using basic trigonometric differentiation rules.
💡 Why this works: The Power Rule is used for the x term, as it is of the form x^1, and the derivative of sin x is a standard result from trigonometric differentiation.
To differentiate x, we apply the Power Rule. The derivative of x^1 is 1. For sin x, we apply the known derivative rule: d/dx[sin x] = cos x.
💡 Why this works: Using these rules, we differentiate each term individually. The derivative of x is 1, and the derivative of sin x is cos x.
The result of applying the rules is f'(x) = 1 + cos x. This is the simplified form of the derivative.
💡 Why this works: The derivative 1 + cos x accurately represents the rate of change of the function x + sin x. Each rule has been applied correctly to produce this final result.
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❌ 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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