Question

find the derivative of ( f(x) ).

( f(x)=cos (x)+sin (x) )

( f^{prime}(x)= )

Explanation:

Step1: Recall derivative rules

The derivative of \(\cos(x)\) is \(-\sin(x)\), and the derivative of \(\sin(x)\) is \(\cos(x)\).

Step2: Apply sum rule

For \(f(x)=\cos(x)+\sin(x)\), by the sum rule of differentiation (\((u + v)'=u'+v'\)), we differentiate each term separately.
The derivative of \(\cos(x)\) is \(-\sin(x)\) and the derivative of \(\sin(x)\) is \(\cos(x)\). So \(f'(x)=-\sin(x)+\cos(x)\).

Answer:

\(-\sin(x) + \cos(x)\)