Answer:
{a,b} = {50,75}
Step-by-step explanation:
Answer:
incorrect because the square area would be 440
Step-by-step explanation:
Answer: ![\dfrac{x^2}{(x^3+1)}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%5E2%7D%7B%28x%5E3%2B1%29%7D)
Step-by-step explanation
Properties of derivative , we use here :
The given function : ![y=\ln(x^3+1)^{\frac{1}{3}}](https://tex.z-dn.net/?f=y%3D%5Cln%28x%5E3%2B1%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D)
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Now , Differentiate both sides , we get
![\dfrac{dy}{dx}=\dfrac{1}{3}\cdot \dfrac{1}{(x^3+1)}\cdot \dfrac{d}{dx}(x^3+1)](https://tex.z-dn.net/?f=%5Cdfrac%7Bdy%7D%7Bdx%7D%3D%5Cdfrac%7B1%7D%7B3%7D%5Ccdot%20%5Cdfrac%7B1%7D%7B%28x%5E3%2B1%29%7D%5Ccdot%20%5Cdfrac%7Bd%7D%7Bdx%7D%28x%5E3%2B1%29)
(By chain rule)
![=\dfrac{1}{3}\cdot \dfrac{1}{(x^3+1)}\cdot (3x^2+0)](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B1%7D%7B3%7D%5Ccdot%20%5Cdfrac%7B1%7D%7B%28x%5E3%2B1%29%7D%5Ccdot%20%283x%5E2%2B0%29)
![=\dfrac{1}{3}\cdot \dfrac{1}{(x^3+1)}(3x^2)](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B1%7D%7B3%7D%5Ccdot%20%5Cdfrac%7B1%7D%7B%28x%5E3%2B1%29%7D%283x%5E2%29)
![=\dfrac{x^2}{(x^3+1)}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7Bx%5E2%7D%7B%28x%5E3%2B1%29%7D)
Hence, the derivative of the function will be : ![\dfrac{x^2}{(x^3+1)}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%5E2%7D%7B%28x%5E3%2B1%29%7D)