The derivative of [tex]f[/tex] is
[tex]f'(x)=\left(2x^{-1/3}+3\cos x+x^\pi\right)'[/tex]
[tex]f'(x)=\left(2x^{-1/3}\right)'+(3\cos x)'+\left(x^\pi\right)'[/tex]
By the power rule,
[tex]f'(x)=-\dfrac23x^{-4/3}+(3\cos x)'+\pi x^{\pi-1}[/tex]
The derivative of [tex]\cos x[/tex] is [tex]-\sin x[/tex]:
[tex]f'(x)=-\dfrac23x^{-4/3}-3\sin x+\pi x^{\pi-1}[/tex]
