Question
Solve the equation
Solve for x
Solve for y
x=−∣y∣66y5,y=0x=∣y∣66y5,y=0
Evaluate
x6y=6
Rewrite the expression
yx6=6
Divide both sides
yyx6=y6
Divide the numbers
x6=y6
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±6y6
Simplify the expression
More Steps

Evaluate
6y6
To take a root of a fraction,take the root of the numerator and denominator separately
6y66
Multiply by the Conjugate
6y×6y566×6y5
Calculate
∣y∣66×6y5
The product of roots with the same index is equal to the root of the product
∣y∣66y5
x=±∣y∣66y5
Separate the equation into 2 possible cases
x=∣y∣66y5x=−∣y∣66y5
Calculate
{x=−∣y∣66y5y=0{x=∣y∣66y5y=0
Solution
x=−∣y∣66y5,y=0x=∣y∣66y5,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
x6y=6
To test if the graph of x6y=6 is symmetry with respect to the origin,substitute -x for x and -y for y
(−x)6(−y)=6
Evaluate
More Steps

Evaluate
(−x)6(−y)
Rewrite the expression
x6(−y)
Use the commutative property to reorder the terms
−x6y
−x6y=6
Solution
Not symmetry with respect to the origin
Show Solution

Rewrite the equation
r=76sec6(θ)csc(θ)
Evaluate
x6y=6
To convert the equation to polar coordinates,substitute x for rcos(θ) and y for rsin(θ)
(cos(θ)×r)6sin(θ)×r=6
Factor the expression
cos6(θ)sin(θ)×r7=6
Divide the terms
r7=cos6(θ)sin(θ)6
Simplify the expression
r7=6sec6(θ)csc(θ)
Solution
r=76sec6(θ)csc(θ)
Show Solution

Find the first derivative
Find the derivative with respect to x
Find the derivative with respect to y
dxdy=−x6y
Calculate
x6y=6
Take the derivative of both sides
dxd(x6y)=dxd(6)
Calculate the derivative
More Steps

Evaluate
dxd(x6y)
Use differentiation rules
dxd(x6)×y+x6×dxd(y)
Use dxdxn=nxn−1 to find derivative
6x5y+x6×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
6x5y+x6dxdy
6x5y+x6dxdy=dxd(6)
Calculate the derivative
6x5y+x6dxdy=0
Move the expression to the right-hand side and change its sign
x6dxdy=0−6x5y
Removing 0 doesn't change the value,so remove it from the expression
x6dxdy=−6x5y
Divide both sides
x6x6dxdy=x6−6x5y
Divide the numbers
dxdy=x6−6x5y
Solution
More Steps

Evaluate
x6−6x5y
Reduce the fraction
More Steps

Evaluate
x6x5
Use the product rule aman=an−m to simplify the expression
x6−51
Subtract the terms
x11
Simplify
x1
x−6y
Use b−a=−ba=−ba to rewrite the fraction
−x6y
dxdy=−x6y
Show Solution

Find the second derivative
Find the second derivative with respect to x
Find the second derivative with respect to y
dx2d2y=x242y
Calculate
x6y=6
Take the derivative of both sides
dxd(x6y)=dxd(6)
Calculate the derivative
More Steps

Evaluate
dxd(x6y)
Use differentiation rules
dxd(x6)×y+x6×dxd(y)
Use dxdxn=nxn−1 to find derivative
6x5y+x6×dxd(y)
Evaluate the derivative
More Steps

Evaluate
dxd(y)
Use differentiation rules
dyd(y)×dxdy
Use dxdxn=nxn−1 to find derivative
dxdy
6x5y+x6dxdy
6x5y+x6dxdy=dxd(6)
Calculate the derivative
6x5y+x6dxdy=0
Move the expression to the right-hand side and change its sign
x6dxdy=0−6x5y
Removing 0 doesn't change the value,so remove it from the expression
x6dxdy=−6x5y
Divide both sides
x6x6dxdy=x6−6x5y
Divide the numbers
dxdy=x6−6x5y
Divide the numbers
More Steps

Evaluate
x6−6x5y
Reduce the fraction
More Steps

Evaluate
x6x5
Use the product rule aman=an−m to simplify the expression
x6−51
Subtract the terms
x11
Simplify
x1
x−6y
Use b−a=−ba=−ba to rewrite the fraction
−x6y
dxdy=−x6y
Take the derivative of both sides
dxd(dxdy)=dxd(−x6y)
Calculate the derivative
dx2d2y=dxd(−x6y)
Use differentiation rules
dx2d2y=−x2dxd(6y)×x−6y×dxd(x)
Calculate the derivative
More Steps

Evaluate
dxd(6y)
Simplify
6×dxd(y)
Calculate
6dxdy
dx2d2y=−x26dxdy×x−6y×dxd(x)
Use dxdxn=nxn−1 to find derivative
dx2d2y=−x26dxdy×x−6y×1
Use the commutative property to reorder the terms
dx2d2y=−x26xdxdy−6y×1
Any expression multiplied by 1 remains the same
dx2d2y=−x26xdxdy−6y
Use equation dxdy=−x6y to substitute
dx2d2y=−x26x(−x6y)−6y
Solution
More Steps

Calculate
−x26x(−x6y)−6y
Multiply
More Steps

Multiply the terms
6x(−x6y)
Any expression multiplied by 1 remains the same
−6x×x6y
Multiply the terms
−36y
−x2−36y−6y
Subtract the terms
More Steps

Simplify
−36y−6y
Collect like terms by calculating the sum or difference of their coefficients
(−36−6)y
Subtract the numbers
−42y
−x2−42y
Divide the terms
−(−x242y)
Calculate
x242y
dx2d2y=x242y
Show Solution
