Question

Check my work(derivatives):
find f'(0)
f(x) = x+ sin(2x)
1 + Dsin(2x)
1+ dsin(2x) * d2x
2cos(2x) + 1
2cos(2*0) + 1 = 3

Answer 1

Differentiate \(f\):$$f(x)=x+\sin2x\\f'(x)=\frac{d}{dx}[x+\sin2x]=\frac{d}{dx}x+\frac{d}{dx}\sin2x\\\ \ \ \ \ \ \ \ =1+2\cos2x\\f'(0)=1+2\cos2(0)=1+2\cos0=1+2=3$$