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Step 1:
Start by putting

in front of each term
![\frac{d}{dx}[y cos x]= \frac{d}{dx}[5x^2]+ \frac{d}{dx}[ 3y^2]](https://tex.z-dn.net/?f=%20%5Cfrac%7Bd%7D%7Bdx%7D%5By%20cos%20x%5D%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5B5x%5E2%5D%2B%20%5Cfrac%7Bd%7D%7Bdx%7D%5B%203y%5E2%5D)
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Step 2:
Deal with the terms in 'x' and the constant terms
![\frac{d}{dx}[ycosx]= 10x+ \frac{d}{dx} [3y^2]](https://tex.z-dn.net/?f=%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bycosx%5D%3D%2010x%2B%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5B3y%5E2%5D%20%20)
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Step 3:
Use the chain rule for the terms in 'y'
![\frac{d}{dx}[ycosx]=10x+6y \frac{dy}{dx}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bycosx%5D%3D10x%2B6y%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%20)
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Step 4:
Use the product rule on the term in 'x' and 'y'


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Step 5:
Rearrange to make

the subject


![[cos(x) - 6y] \frac{dy}{dx}=10x + y sin(y)](https://tex.z-dn.net/?f=%5Bcos%28x%29%20-%206y%5D%20%20%5Cfrac%7Bdy%7D%7Bdx%7D%3D10x%20%2B%20y%20sin%28y%29%20)

⇒ Final Answer
Answer:
The equation is:
An identity
Has infinitely many solutions
No solution
Step-by-step explanation:
Because there is integers on both sides, we know that any attempts to fix this will either cause an identity, or a false numerical equation(an identity but <em>w r o n g</em>).(Note, an identity can either mean 2 = 2 or x = x).
Identities have infinite solutions, because it does not matter what you put in, the equation will always be true. False equations do not have a solution because they aren't even true equations.
Hope this helps!
Step-by-step explanation and answer:
For this you just need to plug in x for y = f(1/5x)
1/5(-4) = -4/5 or -0.8
1/5(-1) = -1/5 or -0.2
1/5(0) = 0
1/5(3) = 3/5 or 0.6
1/5(6) = 6/5 or 1.2 or 1 1/5
First see you can factor out 4. What is left is x^2 + 6x - 16.
That can be factored as (x+8)(x-2) so the total factorization is
4(x+8)(x-2)