xy^2+xy=8x then by points (1,2) what is dy/du?
- 1/2
- 2/5
- 5/2
- 4/5
Explanation
You gave the equation:
xy² + xy = 8x
We are to find dy/dx at the point (1, 2).
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Step 1: Differentiate both sides implicitly with respect to x:
d/dx(xy²) + d/dx(xy) = d/dx(8x)
Use product rule:
d/dx(xy²) = x·d/dx(y²) + y²·d/dx(x) = x·2y·dy/dx + y²
d/dx(xy) = x·dy/dx + y
d/dx(8x) = 8
So the full derivative becomes:
x·2y·dy/dx + y² + x·dy/dx + y = 8
Now plug in x = 1, y = 2:
1·2·2·dy/dx + 4 + 1·dy/dx + 2 = 8
=> 4·dy/dx + 4 + dy/dx + 2 = 8
=> 5·dy/dx + 6 = 8
=> 5·dy/dx = 2
=> dy/dx = 2/5
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