Find the Derivative - d/dx y=cos(x)-sin(x)

Problem

d()/d(x)*(cos(x)−sin(x))

Solution

1. Identify the expression as a difference of two trigonometric functions.

2. Apply the sum/difference rule for derivatives, which states that the derivative of a sum or difference is the sum or difference of the derivatives.

3. Differentiate the first term using the rule d(cos(x))/d(x)=−sin(x)

4. Differentiate the second term using the rule d(sin(x))/d(x)=cos(x)

5. Combine the results to find the final derivative.

Final Answer

d()/d(x)*(cos(x)−sin(x))=−sin(x)−cos(x)

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