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

Problem

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

Solution

1. Apply the sum rule for differentiation, which states that the derivative of a sum is the sum of the derivatives.

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

2. Differentiate the first term using the trigonometric derivative rule for sine.

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

3. Differentiate the second term using the trigonometric derivative rule for cosine.

d(cos(x))/d(x)=−sin(x)

4. Combine the results to find the final derivative of the function.

cos(x)+(−sin(x))=cos(x)−sin(x)

Final Answer

(d(sin(x))+cos(x))/d(x)=cos(x)−sin(x)

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