Learn how to find the derivative of x + cos x. The derivative is d/dx[x + cos x].
Below is the graph of f(x) = x + cos 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 + cos x consists of two parts: a linear term (x) and a trigonometric term (cos x). The Power Rule is used to differentiate the linear term, while the derivative of cos x requires a standard rule from trigonometry.
💡 Why this works: We apply the Power Rule to differentiate the linear term 'x' and use the known derivative for cos x to handle the trigonometric term.
To differentiate x + cos x, apply the Power Rule to the x term. The derivative of x with respect to x is simply 1. For cos x, we use the rule d/dx[cos x] = -sin x. Hence, the derivative of x + cos x is the sum of these results.
💡 Why this works: After differentiating both terms, we get f'(x) = 1 - sin x, which is the derivative of x + cos x.
The expression for the derivative, f'(x) = 1 - sin x, is already in its simplest form. We can verify the result by checking the derivative rules and confirming that the differentiation was performed correctly.
💡 Why this works: The derivative d/dx[x + cos x] = 1 - sin x is the correct and simplified result. There are no further simplifications needed.
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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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