15. if ( f(x)=x+sin x ), then ( f^{prime}(x)= )
15. if ( f(x)=x+sin x ), then ( f^{prime}(x)= )
Answer
Explanation:
Step1: Differentiate (x)
The derivative of (x) with respect to (x) is (1).
Step2: Differentiate (\sin x)
The derivative of (\sin x) with respect to (x) is (\cos x).
Step3: Apply sum rule of differentiation
If (f(x)=u(x)+v(x)), then (f^{\prime}(x)=u^{\prime}(x)+v^{\prime}(x)). Here (u(x) = x) and (v(x)=\sin x). So (f^{\prime}(x)=\frac{d}{dx}(x)+\frac{d}{dx}(\sin x)).
Answer:
(1 + \cos x)