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

Problem

d()/d(x)*(sin(x)−cos(x))

Solution

1. Apply the sum/difference rule for derivatives, which allows for the differentiation of each term independently.

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

2. Differentiate the first term using the trigonometric derivative rule where the derivative of sin(x) is cos(x)

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

3. Differentiate the second term using the trigonometric derivative rule where the derivative of cos(x) is −sin(x)

d(cos(x))/d(x)=−sin(x)

4. Combine the results and simplify the signs.

cos(x)−(−sin(x))=cos(x)+sin(x)

Final Answer

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

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