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Answer :
Final answer:
The derivative of f(x) = (7x⁵ - 4) / (3x² - 2) is (63x⁶ - 70x⁴ + 24x) / ((3x² - 2)²).
Explanation:
To find the derivative of f(x) = (7x⁵ - 4) / (3x² - 2), we will use the quotient rule. The quotient rule states that if we have a function in the form of f(x) = g(x) / h(x), where both g(x) and h(x) are differentiable functions, then the derivative of f(x) is given by:
f'(x) = (h(x)g'(x) - g(x)h'(x)) / (h(x))²
Using the quotient rule, we can differentiate f(x) step by step:
- Find the derivatives of 7x⁵ - 4 and 3x² - 2.
- Plug the derivatives into the quotient rule formula.
- Simplify the expression to get the final result.
After simplifying the expression, we obtain the derivative of f(x) as:
f'(x) = (63x⁶ - 70x⁴ + 24x) / ((3x² - 2)²)
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