Answer:
dy/dx = ( 2x - y^2 - 1) / (3y^2 + 2xy + 1).
Step-by-step explanation:
Cross multiply:
x^2 = (x + y)(y^2 + 1)
Using the Chain and Product rules:
Finding the derivative:
2x = (x + y)(2y dy/dx) + (y^2 + 1)(1 + dy/dx)
2x = 2xy dy/dx + 2y^2 dy/dx + y^2 + y^2 dy/dx + 1 + dy/dx
2xy dy/dx + 2y^2 dy/dx + y^2 dy/dx + dy/dx = 2x - y^2 - 1
3y^2 dy/dx + 2xy dy/dx + dy/dx = 2x - y^2 - 1
dy/dx = ( 2x - y^2 - 1) / (3y^2 + 2xy + 1).
Answer:
1/36
Step-by-step explanation:
Getting a 3 is 1/6
Getting a 5 is 1/6
Multiply those and get 1/36
3(x)+3=36
-3 -3
3(x)=33
3 3
x=11
Answer:
- Powers of the variable descending left to right
- right side of the equal sign is 0
Step-by-step explanation:
For some constants a, b, and c, the standard form* is ...
ax^2 + bx + c = 0
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It is nice if the leading coefficient (a) is positive, but that is not required.
The main ideas are that ...
- Powers of the variable are descending
- All of the non-zero terms are on the left side of the equal sign
- Like terms are combined
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* This is the <em>standard form</em> for a quadratic. For other kinds of equations, when the expression is equal to zero, this would be called "general form."