Question
Solve the equation
Solve for x
Solve for y
x=7y3196y2
Evaluate
7x3y=4
Rewrite the expression
7yx3=4
Divide both sides
7y7yx3=7y4
Divide the numbers
x3=7y4
Take the 3-th root on both sides of the equation
3x3=37y4
Calculate
x=37y4
Solution
More Steps

Evaluate
37y4
To take a root of a fraction,take the root of the numerator and denominator separately
37y34
Multiply by the Conjugate
37y×372y234×372y2
Calculate
7y34×372y2
Calculate
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Evaluate
34×372y2
The product of roots with the same index is equal to the root of the product
34×72y2
Calculate the product
3196y2
7y3196y2
x=7y3196y2
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
7x3y=4
To test if the graph of 7x3y=4 is symmetry with respect to the origin,substitute -x for x and -y for y
7(−x)3(−y)=4
Evaluate
More Steps

Evaluate
7(−x)3(−y)
Any expression multiplied by 1 remains the same
−7(−x)3y
Multiply the terms
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Evaluate
7(−x)3
Rewrite the expression
7(−x3)
Multiply the numbers
−7x3
−(−7x3y)
Multiply the first two terms
7x3y
7x3y=4
Solution
Symmetry with respect to the origin
Show Solution

Rewrite the equation
r=47cos3(θ)sin(θ)2r=−47cos3(θ)sin(θ)2
Evaluate
7x3y=4
To convert the equation to polar coordinates,substitute x for rcos(θ) and y for rsin(θ)
7(cos(θ)×r)3sin(θ)×r=4
Factor the expression
7cos3(θ)sin(θ)×r4=4
Divide the terms
r4=7cos3(θ)sin(θ)4
Evaluate the power
r=±47cos3(θ)sin(θ)4
Simplify the expression
More Steps

Evaluate
47cos3(θ)sin(θ)4
To take a root of a fraction,take the root of the numerator and denominator separately
47cos3(θ)sin(θ)44
Simplify the radical expression
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Evaluate
44
Write the number in exponential form with the base of 2
422
Reduce the index of the radical and exponent with 2
2
47cos3(θ)sin(θ)2
r=±47cos3(θ)sin(θ)2
Solution
r=47cos3(θ)sin(θ)2r=−47cos3(θ)sin(θ)2
Show Solution

Find the first derivative
Find the derivative with respect to x
Find the derivative with respect to y
dxdy=−x3y
Calculate
7x3y=4
Take the derivative of both sides
dxd(7x3y)=dxd(4)
Calculate the derivative
More Steps

Evaluate
dxd(7x3y)
Use differentiation rules
dxd(7x3)×y+7x3×dxd(y)
Evaluate the derivative
More Steps

Evaluate
dxd(7x3)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
7×dxd(x3)
Use dxdxn=nxn−1 to find derivative
7×3x2
Multiply the terms
21x2
21x2y+7x3×dxd(y)
Evaluate the derivative
More Steps

Evaluate
dxd(y)
Use differentiation rules
dyd(y)×dxdy
Use dxdxn=nxn−1 to find derivative
dxdy
21x2y+7x3dxdy
21x2y+7x3dxdy=dxd(4)
Calculate the derivative
21x2y+7x3dxdy=0
Move the expression to the right-hand side and change its sign
7x3dxdy=0−21x2y
Removing 0 doesn't change the value,so remove it from the expression
7x3dxdy=−21x2y
Divide both sides
7x37x3dxdy=7x3−21x2y
Divide the numbers
dxdy=7x3−21x2y
Solution
More Steps

Evaluate
7x3−21x2y
Cancel out the common factor 7
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
7x3y=4
Take the derivative of both sides
dxd(7x3y)=dxd(4)
Calculate the derivative
More Steps

Evaluate
dxd(7x3y)
Use differentiation rules
dxd(7x3)×y+7x3×dxd(y)
Evaluate the derivative
More Steps

Evaluate
dxd(7x3)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
7×dxd(x3)
Use dxdxn=nxn−1 to find derivative
7×3x2
Multiply the terms
21x2
21x2y+7x3×dxd(y)
Evaluate the derivative
More Steps

Evaluate
dxd(y)
Use differentiation rules
dyd(y)×dxdy
Use dxdxn=nxn−1 to find derivative
dxdy
21x2y+7x3dxdy
21x2y+7x3dxdy=dxd(4)
Calculate the derivative
21x2y+7x3dxdy=0
Move the expression to the right-hand side and change its sign
7x3dxdy=0−21x2y
Removing 0 doesn't change the value,so remove it from the expression
7x3dxdy=−21x2y
Divide both sides
7x37x3dxdy=7x3−21x2y
Divide the numbers
dxdy=7x3−21x2y
Divide the numbers
More Steps

Evaluate
7x3−21x2y
Cancel out the common factor 7
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
More Steps

Calculate
−x23x(−x3y)−3y
Multiply
More Steps

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
More Steps

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
