Algebra
Calculus
Trigonometry
Matrix
Question
Solve the equation
y=4x2x−x22x
Evaluate
x2+(y2x)×2=1
Remove the parentheses
x2+y2x×2=1
Use the commutative property to reorder the terms
x2+2y2x=1
Rewrite the expression
x2+22x×y=1
Move the expression to the right-hand side and change its sign
22x×y=1−x2
Divide both sides
22x22x×y=22x1−x2
Divide the numbers
y=22x1−x2
Solution
More Steps
Evaluate
22x1−x2
Multiply by the Conjugate
22x×2x(1−x2)2x
Calculate
2×2x(1−x2)2x
Calculate
More Steps
Evaluate
(1−x2)2x
Multiply each term in the parentheses by 2x
1×2x−x22x
Calculate the product
2x−x22x
2×2x2x−x22x
Calculate
4x2x−x22x
y=4x2x−x22x
Show Solution
Testing for symmetry
Testing for symmetry about the origin
Testing for symmetry about the x-axis
Testing for symmetry about the y-axis
Not symmetry with respect to the origin
Evaluate
x2+(y2x)×2=1
Remove the parentheses
x2+y2x×2=1
Use the commutative property to reorder the terms
x2+2y2x=1
To test if the graph of x2+2y2x=1 is symmetry with respect to the origin,substitute -x for x and -y for y
(−x)2+2(−y)2(−x)=1
Evaluate
More Steps
Evaluate
(−x)2+2(−y)2(−x)
Multiply the numbers
(−x)2+2(−y)−2x
Multiply the first two terms
(−x)2−2y−2x
Rewrite the expression
x2−2y−2x
x2−2y−2x=1
Solution
Not symmetry with respect to the origin
Show Solution
Find the first derivative
Find the derivative with respect to x
Find the derivative with respect to y
dxdy=−2xx2x+y
Calculate
x2+(y2x)2=1
Simplify the expression
x2+2y2x=1
Take the derivative of both sides
dxd(x2+2y2x)=dxd(1)
Calculate the derivative
More Steps
Evaluate
dxd(x2+2y2x)
Use differentiation rules
dxd(x2)+dxd(2y2x)
Use dxdxn=nxn−1 to find derivative
2x+dxd(2y2x)
Evaluate the derivative
More Steps
Evaluate
dxd(2y2x)
Use differentiation rules
dxd(2)×y2x+2×dxd(y)×2x+2y×dxd(2x)
Evaluate the derivative
dxd(2)×y2x+2dxdy×2x+2y×dxd(2x)
Evaluate the derivative
dxd(2)×y2x+2dxdy×2x+2x2y
Calculate
2dxdy×2x+2x2y
2x+2dxdy×2x+2x2y
Calculate
2x2x2x+4xdxdy+2y
2x2x2x+4xdxdy+2y=dxd(1)
Calculate the derivative
2x2x2x+4xdxdy+2y=0
Rewrite the expression
2x2x2x+2y+4xdxdy=0
Simplify
2x2x+2y+4xdxdy=0
Move the constant to the right side
4xdxdy=0−(2x2x+2y)
Subtract the terms
More Steps
Evaluate
0−(2x2x+2y)
Removing 0 doesn't change the value,so remove it from the expression
−(2x2x+2y)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−2x2x−2y
4xdxdy=−2x2x−2y
Divide both sides
4x4xdxdy=4x−2x2x−2y
Divide the numbers
dxdy=4x−2x2x−2y
Solution
More Steps
Evaluate
4x−2x2x−2y
Rewrite the expression
4x2(−x2x−y)
Cancel out the common factor 2
2x−x2x−y
Use b−a=−ba=−ba to rewrite the fraction
−2xx2x+y
dxdy=−2xx2x+y
Show Solution