Parallel should be your answer!
Step-by-step explanation:
Let
where
![f(x) = x^4](https://tex.z-dn.net/?f=f%28x%29%20%3D%20x%5E4)
![g(x)= (1 -2x^5)^6](https://tex.z-dn.net/?f=g%28x%29%3D%20%281%20-2x%5E5%29%5E6)
![h(x)= (5 - 8x^3)^2](https://tex.z-dn.net/?f=h%28x%29%3D%20%285%20-%208x%5E3%29%5E2)
so that
![y(x) = x^4(1 -2x^5)^6(5 - 8x^3)^2](https://tex.z-dn.net/?f=y%28x%29%20%3D%20x%5E4%281%20-2x%5E5%29%5E6%285%20-%208x%5E3%29%5E2)
Recall that the derivative of the product of functions is
![y'(x)=f'(x)g(x)h(x)+f(x)g'(x)h(x)+f(x)g(x)h'(x)](https://tex.z-dn.net/?f=y%27%28x%29%3Df%27%28x%29g%28x%29h%28x%29%2Bf%28x%29g%27%28x%29h%28x%29%2Bf%28x%29g%28x%29h%27%28x%29)
so taking the derivatives of the individual functions, we get
![f'(x) = 4x^3](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%204x%5E3)
![g'(x) = 6(1 - 2x^5)^5(-10x^4)](https://tex.z-dn.net/?f=g%27%28x%29%20%3D%206%281%20-%202x%5E5%29%5E5%28-10x%5E4%29)
![h'(x) = 2(5 - 8x^3)(-24x^2)](https://tex.z-dn.net/?f=h%27%28x%29%20%3D%202%285%20-%208x%5E3%29%28-24x%5E2%29)
So the derivative of y(x) is given by
![y'(x) = 4x^3(1 -2x^5)^6(5 - 8x^3)^2 + x^4 6(1 -2x^5)^5(-10x^4)(5 - 8x^3)^2 + x^4(1 -2x^5)^6 2(5 - 8x^3)(-24x^2)](https://tex.z-dn.net/?f=y%27%28x%29%20%3D%204x%5E3%281%20-2x%5E5%29%5E6%285%20-%208x%5E3%29%5E2%20%2B%20%20x%5E4%206%281%20-2x%5E5%29%5E5%28-10x%5E4%29%285%20-%208x%5E3%29%5E2%20%2B%20%20x%5E4%281%20-2x%5E5%29%5E6%202%285%20-%208x%5E3%29%28-24x%5E2%29)
or
![y'(x) = 4x^3(1 -2x^5)^6(5 - 8x^3)^2](https://tex.z-dn.net/?f=y%27%28x%29%20%3D%204x%5E3%281%20-2x%5E5%29%5E6%285%20-%208x%5E3%29%5E2)
![\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:- 60x^8(1 -2x^5)^5(5 - 8x^3)^2](https://tex.z-dn.net/?f=%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A-%2060x%5E8%281%20-2x%5E5%29%5E5%285%20-%208x%5E3%29%5E2)
![\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:- 48x^6(1 -2x^5)^6 2(5 - 8x^3)](https://tex.z-dn.net/?f=%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A-%2048x%5E6%281%20-2x%5E5%29%5E6%202%285%20-%208x%5E3%29)
Hello!
![\large\boxed{\frac{dy}{dx}logx = \frac{1}{xln10} }](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7B%5Cfrac%7Bdy%7D%7Bdx%7Dlogx%20%3D%20%5Cfrac%7B1%7D%7Bxln10%7D%20%20%7D)
Recall that:
can be rewritten as:
![log_{10}x](https://tex.z-dn.net/?f=log_%7B10%7Dx)
Use the equation for the derivative of a log expression:
![\frac{dy}{dx}log_{a}u = \frac{1}{ulna} * u'](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7Dlog_%7Ba%7Du%20%3D%20%5Cfrac%7B1%7D%7Bulna%7D%20%2A%20u%27)
Substitute in the values in the expression:
![logx = \frac{1}{xln10} * 1 = \frac{1}{xln10}](https://tex.z-dn.net/?f=logx%20%3D%20%5Cfrac%7B1%7D%7Bxln10%7D%20%2A%201%20%3D%20%5Cfrac%7B1%7D%7Bxln10%7D)
See Quadratic Formula and Determinant's/Delta's formula
Answer: well search It up 1/10
Step-by-step explanation: