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Answer :
Final answer:
The derivative of f(x) = x^(2/3) - 4x^9 - 11x is obtained by applying the power rule, resulting in f'(x) = (2/3)*x^(-1/3) - 36x^8 - 11. The correct answer is f'(x) = (2/3)*x-1/3 - 36x8 - 11.
Explanation:
To find the derivative of the function f(x) = x2/3 - 4x9 - 11x, we will apply the power rule for each term. The power rule states that the derivative of xn is n*xn-1.
Let's differentiate each term one by one:
- The derivative of x2/3 is (2/3)*x2/3-1 = (2/3)*x-1/3.
- The derivative of 4x9 is 9*4x9-1 = 36x8.
- The derivative of 11x is simply 11 because the power of x is 1.
Putting it all together, the final result is:
f'(x) = (2/3)*x-1/3 - 36x8 - 11.
since differentiation is a foundational concept in calculus and can be applied to various functions providing us with rates of change and slopes of tangents among other things.
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