It will take 22.5 min cause 25 divided by 100 wuld be 4 wich then divide 90 with
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Answer:
Step-by-step explanation:
The given function : ![y=\ln(x(x^2 - 1)^{\frac{1}{2}})](https://tex.z-dn.net/?f=y%3D%5Cln%28x%28x%5E2%20-%201%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%29)
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Now , Differentiate both sides with respect to x , we will get
(By Chain rule)
[Note :
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![\dfrac{1}{x}+\dfrac{1}{2}(\dfrac{1}{x^2-1})(2x-0)](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7Bx%7D%2B%5Cdfrac%7B1%7D%7B2%7D%28%5Cdfrac%7B1%7D%7Bx%5E2-1%7D%29%282x-0%29)
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![=\dfrac{1}{x}+\dfrac{1}{2}(\dfrac{1}{x^2-1})(2x) = \dfrac{1}{x}+\dfrac{x}{x^2-1}\\\\\\=\dfrac{(x^2-1)+(x^2)}{x(x^2-1)}\\\\\\=\dfrac{2x^2-1}{x(x^2-1)}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B1%7D%7Bx%7D%2B%5Cdfrac%7B1%7D%7B2%7D%28%5Cdfrac%7B1%7D%7Bx%5E2-1%7D%29%282x%29%20%3D%20%5Cdfrac%7B1%7D%7Bx%7D%2B%5Cdfrac%7Bx%7D%7Bx%5E2-1%7D%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B%28x%5E2-1%29%2B%28x%5E2%29%7D%7Bx%28x%5E2-1%29%7D%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B2x%5E2-1%7D%7Bx%28x%5E2-1%29%7D)
Hence, the derivative of the given function is
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Answer:
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