Learn how to find the derivative of sin x + cos x. The derivative is d/dx[sin x + cos x].
Below is the graph of f(x) = sin 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.
sin x + cos x is a sum of two trigonometric functions, sin x and cos x. Each function is differentiable using standard trigonometric rules, but the Power Rule is fundamental in understanding the individual derivatives.
💡 Why this works: The Power Rule applies here in the sense that both sin x and cos x are treated individually, as they each follow standard differentiation rules. This makes the differentiation process straightforward.
To find the derivative, apply the derivative rules for sin x and cos x separately. The derivative of sin x is cos x, and the derivative of cos x is -sin x.
💡 Why this works: Thus, d/dx[sin x + cos x] = cos x - sin x. This simple yet essential step demonstrates how the function’s rate of change is determined.
The derivative, d/dx[sin x + cos x], simplifies to cos x - sin x. This is the final form of the derivative.
💡 Why this works: This result is accurate because each term of the sum was differentiated independently, and the rules for sin x and cos x were applied correctly.
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[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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