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What is the derivative of f(x) = sin(x) + cos(x)?
What is the derivative of f(x) = sin(x) + cos(x)?
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Q1
What is the derivative of f(x) = sin(x) + cos(x)?
cos(x) - sin(x)
-sin(x) - cos(x)
sin(x) + cos(x)
-sin(x) + cos(x)
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Using the derivatives of sine and cosine, f'(x) = cos(x) - sin(x).
Questions & Step-by-step Solutions
1 item
Q
Q: What is the derivative of f(x) = sin(x) + cos(x)?
Solution:
Using the derivatives of sine and cosine, f'(x) = cos(x) - sin(x).
Steps: 6
Show Steps
Step 1: Identify the function f(x) = sin(x) + cos(x).
Step 2: Recall the derivative of sin(x), which is cos(x).
Step 3: Recall the derivative of cos(x), which is -sin(x).
Step 4: Apply the derivative rules: the derivative of f(x) is the derivative of sin(x) plus the derivative of cos(x).
Step 5: Combine the results: f'(x) = cos(x) + (-sin(x)).
Step 6: Simplify the expression: f'(x) = cos(x) - sin(x).
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