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