Lời giải:
Ta có: \(f(x)=\sin ^4x+\cos ^4x=(\sin ^2x)^2+(\cos ^2x)^2+2\sin ^2x\cos ^2x-2\sin ^2x\cos ^2x\)
\(=(\sin ^2x+\cos ^2x)^2-\frac{1}{2}(2\sin x\cos x)^2\)
\(=1-\frac{1}{2}\sin ^2(2x)\)
Do đó: \(f'(x)=[1-\frac{1}{2}\sin ^2(2x)]'=-\frac{1}{2}.2.\sin 2x(\sin 2x)'\)
\(=-2\sin 2x.\cos 2x=-\sin 4x\)
Và: \(g(x)=\frac{1}{4}(\cos 4x)\Rightarrow g'(x)=\frac{1}{4}.(4x)'-\sin (4x)=-\sin 4x\)
Do đó: \(f'(x)=g'(x)\)