Algebra
Calculus
Trigonometry
Matrix
Question
Solve the equation
Solve for x
Solve for y
x=∣y∣×1−y2x=−∣y∣×1−y2
Evaluate
y4=y2−x2
Swap the sides of the equation
y2−x2=y4
Move the expression to the right-hand side and change its sign
−x2=y4−y2
Change the signs on both sides of the equation
x2=−y4+y2
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±−y4+y2
Simplify the expression
More Steps
Evaluate
−y4+y2
Factor the expression
y2(1−y2)
The root of a product is equal to the product of the roots of each factor
y2×1−y2
Reduce the index of the radical and exponent with 2
∣y∣×1−y2
x=±(∣y∣×1−y2)
Solution
x=∣y∣×1−y2x=−∣y∣×1−y2
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
Symmetry with respect to the origin
Evaluate
y4=y2−x2
To test if the graph of y4=y2−x2 is symmetry with respect to the origin,substitute -x for x and -y for y
(−y)4=(−y)2−(−x)2
Evaluate
y4=(−y)2−(−x)2
Evaluate
More Steps
Evaluate
(−y)2−(−x)2
Rewrite the expression
y2−(−x)2
Rewrite the expression
y2−x2
y4=y2−x2
Solution
Symmetry with respect to the origin
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Find the first derivative
Find the derivative with respect to x
Find the derivative with respect to y
dxdy=−2y3−yx
Calculate
y4=y2−x2
Take the derivative of both sides
dxd(y4)=dxd(y2−x2)
Calculate the derivative
More Steps
Evaluate
dxd(y4)
Use differentiation rules
dyd(y4)×dxdy
Use dxdxn=nxn−1 to find derivative
4y3dxdy
4y3dxdy=dxd(y2−x2)
Calculate the derivative
More Steps
Evaluate
dxd(y2−x2)
Use differentiation rules
dxd(y2)+dxd(−x2)
Evaluate the derivative
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Evaluate
dxd(y2)
Use differentiation rules
dyd(y2)×dxdy
Use dxdxn=nxn−1 to find derivative
2ydxdy
2ydxdy+dxd(−x2)
Evaluate the derivative
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Evaluate
dxd(−x2)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
−dxd(x2)
Use dxdxn=nxn−1 to find derivative
−2x
2ydxdy−2x
4y3dxdy=2ydxdy−2x
Move the variable to the left side
4y3dxdy−2ydxdy=−2x
Collect like terms by calculating the sum or difference of their coefficients
(4y3−2y)dxdy=−2x
Divide both sides
4y3−2y(4y3−2y)dxdy=4y3−2y−2x
Divide the numbers
dxdy=4y3−2y−2x
Solution
More Steps
Evaluate
4y3−2y−2x
Rewrite the expression
2(2y3−y)−2x
Cancel out the common factor 2
2y3−y−x
Use b−a=−ba=−ba to rewrite the fraction
−2y3−yx
dxdy=−2y3−yx
Show Solution