Answer:
![f_x(x,y,z)=4\sin (y-z)](https://tex.z-dn.net/?f=f_x%28x%2Cy%2Cz%29%3D4%5Csin%20%28y-z%29)
![f_x(x,y,z)=4x\cos (y-z)](https://tex.z-dn.net/?f=f_x%28x%2Cy%2Cz%29%3D4x%5Ccos%20%28y-z%29)
![f_z(x,y,z)=-4x\cos (y-z)](https://tex.z-dn.net/?f=f_z%28x%2Cy%2Cz%29%3D-4x%5Ccos%20%28y-z%29)
Step-by-step explanation:
The given function is
![f(x,y,z)=4x\sin (y-z)](https://tex.z-dn.net/?f=f%28x%2Cy%2Cz%29%3D4x%5Csin%20%28y-z%29)
We need to find first partial derivatives of the function.
Differentiate partially w.r.t. x and y, z are constants.
![f_x(x,y,z)=4(1)\sin (y-z)](https://tex.z-dn.net/?f=f_x%28x%2Cy%2Cz%29%3D4%281%29%5Csin%20%28y-z%29)
![f_x(x,y,z)=4\sin (y-z)](https://tex.z-dn.net/?f=f_x%28x%2Cy%2Cz%29%3D4%5Csin%20%28y-z%29)
Differentiate partially w.r.t. y and x, z are constants.
![f_y(x,y,z)=4x\cos (y-z)\dfrac{\partial}{\partial y}(y-z)](https://tex.z-dn.net/?f=f_y%28x%2Cy%2Cz%29%3D4x%5Ccos%20%28y-z%29%5Cdfrac%7B%5Cpartial%7D%7B%5Cpartial%20y%7D%28y-z%29)
![f_y(x,y,z)=4x\cos (y-z)](https://tex.z-dn.net/?f=f_y%28x%2Cy%2Cz%29%3D4x%5Ccos%20%28y-z%29)
Differentiate partially w.r.t. z and x, y are constants.
![f_z(x,y,z)=4x\cos (y-z)\dfrac{\partial}{\partial z}(y-z)](https://tex.z-dn.net/?f=f_z%28x%2Cy%2Cz%29%3D4x%5Ccos%20%28y-z%29%5Cdfrac%7B%5Cpartial%7D%7B%5Cpartial%20z%7D%28y-z%29)
![f_z(x,y,z)=4x\cos (y-z)(-1)](https://tex.z-dn.net/?f=f_z%28x%2Cy%2Cz%29%3D4x%5Ccos%20%28y-z%29%28-1%29)
![f_z(x,y,z)=-4x\cos (y-z)](https://tex.z-dn.net/?f=f_z%28x%2Cy%2Cz%29%3D-4x%5Ccos%20%28y-z%29)
Therefore, the first partial derivatives of the function are
.
4 or less: 4/8 so 1/2
6 or less: 6/8 so 3/4
8 or less: 8/8 so 1
Answer:
![{7a^{5}b^{5} c\\](https://tex.z-dn.net/?f=%7B7a%5E%7B5%7Db%5E%7B5%7D%20c%5C%5C)
Step-by-step explanation:
![\frac{28a^{8}b^{6} c^{3} }{4a^{3}bc^{2} }](https://tex.z-dn.net/?f=%5Cfrac%7B28a%5E%7B8%7Db%5E%7B6%7D%20c%5E%7B3%7D%20%20%7D%7B4a%5E%7B3%7Dbc%5E%7B2%7D%20%20%7D)
→ First look at the first term of each expression and see if they can be simplified, and they can
![\frac{7a^{8}b^{6} c^{3} }{a^{3}bc^{2} }](https://tex.z-dn.net/?f=%5Cfrac%7B7a%5E%7B8%7Db%5E%7B6%7D%20c%5E%7B3%7D%20%20%7D%7Ba%5E%7B3%7Dbc%5E%7B2%7D%20%20%7D)
→ Now look at the a terms, since a larger one is at the top, you subtract
![\frac{7a^{5}b^{6} c^{3} }{bc^{2} }](https://tex.z-dn.net/?f=%5Cfrac%7B7a%5E%7B5%7Db%5E%7B6%7D%20c%5E%7B3%7D%20%20%7D%7Bbc%5E%7B2%7D%20%20%7D)
→ Now simplify the b and c terms
![{7a^{5}b^{5} c](https://tex.z-dn.net/?f=%7B7a%5E%7B5%7Db%5E%7B5%7D%20c)
Answer:
i sowwy
Step-by-step explanation: