Find the third derivative of the given function. \[ f(x)=4 x^{5}-3 x^{4}+4 x^{2}-2 x+6 \] \[ f^{n+1}(x)= \]

Step 1 ：Given the function \(f(x)=4 x^{5}-3 x^{4}+4 x^{2}-2 x+6\)

Step 2 ：Find the first derivative using the power rule, \(f'(x)=20x^{4}-12x^{3}+8x-2\)

Step 3 ：Find the second derivative, \(f''(x)=80x^{3}-36x^{2}+8\)

Step 4 ：Finally, find the third derivative, \(f'''(x)=240x^{2}-72x\)

Step 5 ：Final Answer: The third derivative of the function \(f(x)=4 x^{5}-3 x^{4}+4 x^{2}-2 x+6\) is \(\boxed{240x^{2}-72x}\)