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Answer :
The indicated derivative of the function f⁴(x) = 1800x² - 168.
The function f(x) = 5x⁶- 7x⁴ + 4x² is a polynomial function. To find its fourth derivative f⁴(x), we need to differentiate it four times using the power rule of differentiation.
1. First Derivative f'(x):
f'(x) = 30x⁵ - 28x³ + 8x
2. Second Derivative f''(x):
f''(x) = 150x⁴ - 84x² + 8
3. Third Derivative f'''(x):
f'''(x) = 600x³ - 168x
4. Fourth Derivative f⁴(x):
f⁴(x) = 1800x² - 168
Thus, the fourth derivative of f(x) = 5x⁶ - 7x⁴ + 4x² is f⁴(x) = 1800x² - 168.
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