Under which market structure does a firm have negligible influence over product pricing
1 answer:
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Step-by-step explanation:
Notice the two horinzontal lines. They are parallel lines as they will never cross each other.
Notice the slant line. That is called a transversal as it crosses through both the parallel lines.
The transversal split the parallel lines into multiple angles.
- Vertical Angles
- Alternate Interior Angles
- Alternate Exterior Angles
- Corresponding Angles
- Linear Pair Angles
- Same Side Consecutive Angles
Look at Angle X and the angle on the upper right. They are vertical angles because they are formed by intersecting lines so they are equal to each other
Look at Angle X and the angle that is on the right of Angle 70, they are alternate interior angles as they are formed by the transversal crossing through the two parallel lines. They are equal to each other. They form a Z if you connect a them.
The upper right angle and bottom left angle are alternate exterior angles. They are formed by the transversal. They are equal to each other. They form a semi circle of you connect them.
The bottom left angle and Angle X are Corresponding Angles. They form a C shape if you connect them. They are formed by the transversal and are congruent to each other.
Angle X and 70 are same side consecutive angles. They are right next to each other on the same side of each other. They are supplementary. which means they form 180 degrees when added.
so using this info,
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_______________
dy
Find —— for an implicit function:
dx
cos(xy) = 3x + 1.
First, differentiate implicitly both sides with respect to x. Keep in mind that y is not just a variable, but it is also a function of x, so you have to use the chain rule there:
![\mathsf{\dfrac{d}{dx}\big[cos(xy)\big]=\dfrac{d}{dx}(3x+1)}\\\\\\ \mathsf{-\,sin(xy)\cdot \dfrac{d}{dx}(xy)=\dfrac{d}{dx}(3x)+\dfrac{d}{dx}(1)}](https://tex.z-dn.net/?f=%5Cmathsf%7B%5Cdfrac%7Bd%7D%7Bdx%7D%5Cbig%5Bcos%28xy%29%5Cbig%5D%3D%5Cdfrac%7Bd%7D%7Bdx%7D%283x%2B1%29%7D%5C%5C%5C%5C%5C%5C%0A%5Cmathsf%7B-%5C%2Csin%28xy%29%5Ccdot%20%5Cdfrac%7Bd%7D%7Bdx%7D%28xy%29%3D%5Cdfrac%7Bd%7D%7Bdx%7D%283x%29%2B%5Cdfrac%7Bd%7D%7Bdx%7D%281%29%7D)
Apply the product rule to differentiate that term at the left-hand side:
![\mathsf{-\,sin(xy)\cdot \left[\dfrac{d}{dx}(x)\cdot y+x\cdot \dfrac{dy}{dx}\right]=3+0}\\\\\\ \mathsf{-\,sin(xy)\cdot \left[1\cdot y+x\cdot \dfrac{dy}{dx}\right]=3}\\\\\\ \mathsf{-\,sin(xy)\cdot \left[y+x\cdot \dfrac{dy}{dx}\right]=3}](https://tex.z-dn.net/?f=%5Cmathsf%7B-%5C%2Csin%28xy%29%5Ccdot%20%5Cleft%5B%5Cdfrac%7Bd%7D%7Bdx%7D%28x%29%5Ccdot%20y%2Bx%5Ccdot%20%5Cdfrac%7Bdy%7D%7Bdx%7D%5Cright%5D%3D3%2B0%7D%5C%5C%5C%5C%5C%5C%0A%5Cmathsf%7B-%5C%2Csin%28xy%29%5Ccdot%20%5Cleft%5B1%5Ccdot%20y%2Bx%5Ccdot%20%5Cdfrac%7Bdy%7D%7Bdx%7D%5Cright%5D%3D3%7D%5C%5C%5C%5C%5C%5C%0A%5Cmathsf%7B-%5C%2Csin%28xy%29%5Ccdot%20%5Cleft%5By%2Bx%5Ccdot%20%5Cdfrac%7Bdy%7D%7Bdx%7D%5Cright%5D%3D3%7D)
Now, multiply out the terms to get rid of the brackets at the left-hand
dy
side, and then isolate —— :
dx
and there it is.
I hope this helps. =)
Tags: <span><em>implicit function derivative implicit differentiation chain product rule differential integral calculus</em>
</span>
_______________
dy
Find —— for an implicit function:
dx
cos(xy) = 3x + 1.
First, differentiate implicitly both sides with respect to x. Keep in mind that y is not just a variable, but it is also a function of x, so you have to use the chain rule there:
Apply the product rule to differentiate that term at the left-hand side:
Now, multiply out the terms to get rid of the brackets at the left-hand
dy
side, and then isolate —— :
dx
and there it is.
I hope this helps. =)
Tags: <span><em>implicit function derivative implicit differentiation chain product rule differential integral calculus</em>
</span>