Question
Solve the equation
Solve for x
Solve for y
x=y39y2
Evaluate
x3×2(y×1)×2=36
Remove the parentheses
x3×2y×1×2=36
Multiply the terms
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Evaluate
x3×2y×1×2
Rewrite the expression
x3×2y×2
Multiply the terms
x3×4y
Use the commutative property to reorder the terms
4x3y
4x3y=36
Rewrite the expression
4yx3=36
Divide both sides
4y4yx3=4y36
Divide the numbers
x3=4y36
Cancel out the common factor 4
x3=y9
Take the 3-th root on both sides of the equation
3x3=3y9
Calculate
x=3y9
Solution
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Evaluate
3y9
To take a root of a fraction,take the root of the numerator and denominator separately
3y39
Multiply by the Conjugate
3y×3y239×3y2
Calculate
y39×3y2
The product of roots with the same index is equal to the root of the product
y39y2
x=y39y2
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
x3×2(y×1)×2=36
Remove the parentheses
x3×2y×1×2=36
Multiply the terms
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Evaluate
x3×2y×1×2
Rewrite the expression
x3×2y×2
Multiply the terms
x3×4y
Use the commutative property to reorder the terms
4x3y
4x3y=36
To test if the graph of 4x3y=36 is symmetry with respect to the origin,substitute -x for x and -y for y
4(−x)3(−y)=36
Evaluate
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Evaluate
4(−x)3(−y)
Any expression multiplied by 1 remains the same
−4(−x)3y
Multiply the terms
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Evaluate
4(−x)3
Rewrite the expression
4(−x3)
Multiply the numbers
−4x3
−(−4x3y)
Multiply the first two terms
4x3y
4x3y=36
Solution
Symmetry with respect to the origin
Show Solution

Rewrite the equation
r=49sec3(θ)csc(θ)r=−49sec3(θ)csc(θ)
Evaluate
(x3)×2(y×1)×2=36
Evaluate
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Evaluate
x3×2(y×1)×2
Remove the parentheses
x3×2y×1×2
Rewrite the expression
x3×2y×2
Multiply the terms
x3×4y
Use the commutative property to reorder the terms
4x3y
4x3y=36
To convert the equation to polar coordinates,substitute x for rcos(θ) and y for rsin(θ)
4(cos(θ)×r)3sin(θ)×r=36
Factor the expression
4cos3(θ)sin(θ)×r4=36
Divide the terms
r4=cos3(θ)sin(θ)9
Simplify the expression
r4=9sec3(θ)csc(θ)
Evaluate the power
r=±49sec3(θ)csc(θ)
Solution
r=49sec3(θ)csc(θ)r=−49sec3(θ)csc(θ)
Show Solution

Find the first derivative
Find the derivative with respect to x
Find the derivative with respect to y
dxdy=−x3y
Calculate
(x3)2(y1)2=36
Simplify the expression
4x3y=36
Take the derivative of both sides
dxd(4x3y)=dxd(36)
Calculate the derivative
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Evaluate
dxd(4x3y)
Use differentiation rules
dxd(4x3)×y+4x3×dxd(y)
Evaluate the derivative
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Evaluate
dxd(4x3)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
4×dxd(x3)
Use dxdxn=nxn−1 to find derivative
4×3x2
Multiply the terms
12x2
12x2y+4x3×dxd(y)
Evaluate the derivative
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Evaluate
dxd(y)
Use differentiation rules
dyd(y)×dxdy
Use dxdxn=nxn−1 to find derivative
dxdy
12x2y+4x3dxdy
12x2y+4x3dxdy=dxd(36)
Calculate the derivative
12x2y+4x3dxdy=0
Move the expression to the right-hand side and change its sign
4x3dxdy=0−12x2y
Removing 0 doesn't change the value,so remove it from the expression
4x3dxdy=−12x2y
Divide both sides
4x34x3dxdy=4x3−12x2y
Divide the numbers
dxdy=4x3−12x2y
Solution
More Steps

Evaluate
4x3−12x2y
Cancel out the common factor 4
x3−3x2y
Reduce the fraction
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Evaluate
x3x2
Use the product rule aman=an−m to simplify the expression
x3−21
Subtract the terms
x11
Simplify
x1
x−3y
Use b−a=−ba=−ba to rewrite the fraction
−x3y
dxdy=−x3y
Show Solution

Find the second derivative
Find the second derivative with respect to x
Find the second derivative with respect to y
dx2d2y=x212y
Calculate
(x3)2(y1)2=36
Simplify the expression
4x3y=36
Take the derivative of both sides
dxd(4x3y)=dxd(36)
Calculate the derivative
More Steps

Evaluate
dxd(4x3y)
Use differentiation rules
dxd(4x3)×y+4x3×dxd(y)
Evaluate the derivative
More Steps

Evaluate
dxd(4x3)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
4×dxd(x3)
Use dxdxn=nxn−1 to find derivative
4×3x2
Multiply the terms
12x2
12x2y+4x3×dxd(y)
Evaluate the derivative
More Steps

Evaluate
dxd(y)
Use differentiation rules
dyd(y)×dxdy
Use dxdxn=nxn−1 to find derivative
dxdy
12x2y+4x3dxdy
12x2y+4x3dxdy=dxd(36)
Calculate the derivative
12x2y+4x3dxdy=0
Move the expression to the right-hand side and change its sign
4x3dxdy=0−12x2y
Removing 0 doesn't change the value,so remove it from the expression
4x3dxdy=−12x2y
Divide both sides
4x34x3dxdy=4x3−12x2y
Divide the numbers
dxdy=4x3−12x2y
Divide the numbers
More Steps

Evaluate
4x3−12x2y
Cancel out the common factor 4
x3−3x2y
Reduce the fraction
More Steps

Evaluate
x3x2
Use the product rule aman=an−m to simplify the expression
x3−21
Subtract the terms
x11
Simplify
x1
x−3y
Use b−a=−ba=−ba to rewrite the fraction
−x3y
dxdy=−x3y
Take the derivative of both sides
dxd(dxdy)=dxd(−x3y)
Calculate the derivative
dx2d2y=dxd(−x3y)
Use differentiation rules
dx2d2y=−x2dxd(3y)×x−3y×dxd(x)
Calculate the derivative
More Steps

Evaluate
dxd(3y)
Simplify
3×dxd(y)
Calculate
3dxdy
dx2d2y=−x23dxdy×x−3y×dxd(x)
Use dxdxn=nxn−1 to find derivative
dx2d2y=−x23dxdy×x−3y×1
Use the commutative property to reorder the terms
dx2d2y=−x23xdxdy−3y×1
Any expression multiplied by 1 remains the same
dx2d2y=−x23xdxdy−3y
Use equation dxdy=−x3y to substitute
dx2d2y=−x23x(−x3y)−3y
Solution
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Calculate
−x23x(−x3y)−3y
Multiply
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Multiply the terms
3x(−x3y)
Any expression multiplied by 1 remains the same
−3x×x3y
Multiply the terms
−9y
−x2−9y−3y
Subtract the terms
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Simplify
−9y−3y
Collect like terms by calculating the sum or difference of their coefficients
(−9−3)y
Subtract the numbers
−12y
−x2−12y
Divide the terms
−(−x212y)
Calculate
x212y
dx2d2y=x212y
Show Solution
