Question
Solve the equation
Solve for x
Solve for y
x=−∣y∣45y3,y=0x=∣y∣45y3,y=0
Evaluate
2x4y−10=0
Rewrite the expression
2yx4−10=0
Move the constant to the right-hand side and change its sign
2yx4=0+10
Removing 0 doesn't change the value,so remove it from the expression
2yx4=10
Divide both sides
2y2yx4=2y10
Divide the numbers
x4=2y10
Cancel out the common factor 2
x4=y5
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±4y5
Simplify the expression
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Evaluate
4y5
To take a root of a fraction,take the root of the numerator and denominator separately
4y45
Multiply by the Conjugate
4y×4y345×4y3
Calculate
∣y∣45×4y3
The product of roots with the same index is equal to the root of the product
∣y∣45y3
x=±∣y∣45y3
Separate the equation into 2 possible cases
x=∣y∣45y3x=−∣y∣45y3
Calculate
{x=−∣y∣45y3y=0{x=∣y∣45y3y=0
Solution
x=−∣y∣45y3,y=0x=∣y∣45y3,y=0
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
2x4y−10=0
To test if the graph of 2x4y−10=0 is symmetry with respect to the origin,substitute -x for x and -y for y
2(−x)4(−y)−10=0
Evaluate
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Evaluate
2(−x)4(−y)−10
Multiply
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Evaluate
2(−x)4(−y)
Any expression multiplied by 1 remains the same
−2(−x)4y
Multiply the terms
−2x4y
−2x4y−10
−2x4y−10=0
Solution
Not symmetry with respect to the origin
Show Solution

Rewrite the equation
r=55sec4(θ)csc(θ)
Evaluate
2x4y−10=0
To convert the equation to polar coordinates,substitute x for rcos(θ) and y for rsin(θ)
2(cos(θ)×r)4sin(θ)×r−10=0
Factor the expression
2cos4(θ)sin(θ)×r5−10=0
Subtract the terms
2cos4(θ)sin(θ)×r5−10−(−10)=0−(−10)
Evaluate
2cos4(θ)sin(θ)×r5=10
Divide the terms
r5=cos4(θ)sin(θ)5
Simplify the expression
r5=5sec4(θ)csc(θ)
Solution
r=55sec4(θ)csc(θ)
Show Solution

Find the first derivative
Find the derivative with respect to x
Find the derivative with respect to y
dxdy=−x4y
Calculate
2x4y−10=0
Take the derivative of both sides
dxd(2x4y−10)=dxd(0)
Calculate the derivative
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Evaluate
dxd(2x4y−10)
Use differentiation rules
dxd(2x4y)+dxd(−10)
Evaluate the derivative
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Evaluate
dxd(2x4y)
Use differentiation rules
dxd(2x4)×y+2x4×dxd(y)
Evaluate the derivative
8x3y+2x4×dxd(y)
Evaluate the derivative
8x3y+2x4dxdy
8x3y+2x4dxdy+dxd(−10)
Use dxd(c)=0 to find derivative
8x3y+2x4dxdy+0
Evaluate
8x3y+2x4dxdy
8x3y+2x4dxdy=dxd(0)
Calculate the derivative
8x3y+2x4dxdy=0
Move the expression to the right-hand side and change its sign
2x4dxdy=0−8x3y
Removing 0 doesn't change the value,so remove it from the expression
2x4dxdy=−8x3y
Divide both sides
2x42x4dxdy=2x4−8x3y
Divide the numbers
dxdy=2x4−8x3y
Solution
More Steps

Evaluate
2x4−8x3y
Cancel out the common factor 2
x4−4x3y
Reduce the fraction
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Evaluate
x4x3
Use the product rule aman=an−m to simplify the expression
x4−31
Subtract the terms
x11
Simplify
x1
x−4y
Use b−a=−ba=−ba to rewrite the fraction
−x4y
dxdy=−x4y
Show Solution

Find the second derivative
Find the second derivative with respect to x
Find the second derivative with respect to y
dx2d2y=x220y
Calculate
2x4y−10=0
Take the derivative of both sides
dxd(2x4y−10)=dxd(0)
Calculate the derivative
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Evaluate
dxd(2x4y−10)
Use differentiation rules
dxd(2x4y)+dxd(−10)
Evaluate the derivative
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Evaluate
dxd(2x4y)
Use differentiation rules
dxd(2x4)×y+2x4×dxd(y)
Evaluate the derivative
8x3y+2x4×dxd(y)
Evaluate the derivative
8x3y+2x4dxdy
8x3y+2x4dxdy+dxd(−10)
Use dxd(c)=0 to find derivative
8x3y+2x4dxdy+0
Evaluate
8x3y+2x4dxdy
8x3y+2x4dxdy=dxd(0)
Calculate the derivative
8x3y+2x4dxdy=0
Move the expression to the right-hand side and change its sign
2x4dxdy=0−8x3y
Removing 0 doesn't change the value,so remove it from the expression
2x4dxdy=−8x3y
Divide both sides
2x42x4dxdy=2x4−8x3y
Divide the numbers
dxdy=2x4−8x3y
Divide the numbers
More Steps

Evaluate
2x4−8x3y
Cancel out the common factor 2
x4−4x3y
Reduce the fraction
More Steps

Evaluate
x4x3
Use the product rule aman=an−m to simplify the expression
x4−31
Subtract the terms
x11
Simplify
x1
x−4y
Use b−a=−ba=−ba to rewrite the fraction
−x4y
dxdy=−x4y
Take the derivative of both sides
dxd(dxdy)=dxd(−x4y)
Calculate the derivative
dx2d2y=dxd(−x4y)
Use differentiation rules
dx2d2y=−x2dxd(4y)×x−4y×dxd(x)
Calculate the derivative
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Evaluate
dxd(4y)
Simplify
4×dxd(y)
Calculate
4dxdy
dx2d2y=−x24dxdy×x−4y×dxd(x)
Use dxdxn=nxn−1 to find derivative
dx2d2y=−x24dxdy×x−4y×1
Use the commutative property to reorder the terms
dx2d2y=−x24xdxdy−4y×1
Any expression multiplied by 1 remains the same
dx2d2y=−x24xdxdy−4y
Use equation dxdy=−x4y to substitute
dx2d2y=−x24x(−x4y)−4y
Solution
More Steps

Calculate
−x24x(−x4y)−4y
Multiply
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Multiply the terms
4x(−x4y)
Any expression multiplied by 1 remains the same
−4x×x4y
Multiply the terms
−16y
−x2−16y−4y
Subtract the terms
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Simplify
−16y−4y
Collect like terms by calculating the sum or difference of their coefficients
(−16−4)y
Subtract the numbers
−20y
−x2−20y
Divide the terms
−(−x220y)
Calculate
x220y
dx2d2y=x220y
Show Solution
