We have
\(h(x)=\cos (kx)*f(x)+\sin x\)
We take the derivative of \(h(x)\):
\(h'(x)=\cos (kx)*f'(x)+k(-\sin (kx))*f(x)+\cos x\)
Now we simply plug in 0:
\(h'(0)=\cos (k*0)*f'(0)-k\sin (k*0)*f(0)+\cos 0\)
\(=\cos 0 *5-k\sin 0 *3+\cos 0\)
\(=5*1-3k*0+1\)
\(=5+1\)
\(=6\)
