Final answer:
The derivative of the function 10√x + 4/x⁹ is found using the power rule, resulting in (5/x¹¹²) - (36/x¹ⁱ), when not using fractional or negative exponents.
Step-by-step explanation:
The question asks for the derivative of the function 10√x + 4/x⁹, with the answer not in fractional or negative exponents form. Given the relation between roots and exponents, √x can be expressed as x¹¹². To find the derivative of the given function, we will use the power rule. Applying the power rule:
For the term 10√x, the derivative is 10 * (¹¹²)x⁻¹¹². Multiplying by 10, the derivative of this term is 5x⁻¹¹².
For the term 4/x⁹, rewritten as 4x⁻⁹, the derivative is -36x⁻¹ⁱ.
Combining these results, the derivative of our function is 5x⁻¹¹² - 36x⁻¹ⁱ without using fractional or negative exponents. To comply with this condition, we will need to revert the negative exponents back into a divisor format:
The final answer is (5/x¹¹²) - (36/x¹ⁱ).