Find the 2nd Derivative sin(x)+cos(x)

Problem

d2()/(d(x)2)*(sin(x)+cos(x))

Solution

1. Identify the function to be differentiated, which is ƒ(x)=sin(x)+cos(x)

2. Find the first derivative by applying the sum rule and the basic trigonometric derivative rules d(sin(x))/d(x)=cos(x) and d(cos(x))/d(x)=−sin(x)

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

3. Find the second derivative by differentiating the result of the first derivative.

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

4. Factor out the negative sign to simplify the expression.

−sin(x)−cos(x)=−(sin(x)+cos(x))

Final Answer

d2()/(d(x)2)*(sin(x)+cos(x))=−sin(x)−cos(x)

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