Question
Solve the equation
Solve for x
Solve for y
x=y6+3
Evaluate
x−3=y6
Solution
x=y6+3
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
x−3=y6
To test if the graph of x−3=y6 is symmetry with respect to the origin,substitute -x for x and -y for y
−x−3=(−y)6
Evaluate
−x−3=y6
Solution
Not symmetry with respect to the origin
Show Solution

Find the first derivative
Find the derivative with respect to x
Find the derivative with respect to y
dxdy=6y51
Calculate
x−3=y6
Take the derivative of both sides
dxd(x−3)=dxd(y6)
Calculate the derivative
More Steps

Evaluate
dxd(x−3)
Use differentiation rules
dxd(x)+dxd(−3)
Use dxdxn=nxn−1 to find derivative
1+dxd(−3)
Use dxd(c)=0 to find derivative
1+0
Evaluate
1
1=dxd(y6)
Calculate the derivative
More Steps

Evaluate
dxd(y6)
Use differentiation rules
dyd(y6)×dxdy
Use dxdxn=nxn−1 to find derivative
6y5dxdy
1=6y5dxdy
Swap the sides of the equation
6y5dxdy=1
Divide both sides
6y56y5dxdy=6y51
Solution
dxdy=6y51
Show Solution

Find the second derivative
Find the second derivative with respect to x
Find the second derivative with respect to y
dx2d2y=−36y115
Calculate
x−3=y6
Take the derivative of both sides
dxd(x−3)=dxd(y6)
Calculate the derivative
More Steps

Evaluate
dxd(x−3)
Use differentiation rules
dxd(x)+dxd(−3)
Use dxdxn=nxn−1 to find derivative
1+dxd(−3)
Use dxd(c)=0 to find derivative
1+0
Evaluate
1
1=dxd(y6)
Calculate the derivative
More Steps

Evaluate
dxd(y6)
Use differentiation rules
dyd(y6)×dxdy
Use dxdxn=nxn−1 to find derivative
6y5dxdy
1=6y5dxdy
Swap the sides of the equation
6y5dxdy=1
Divide both sides
6y56y5dxdy=6y51
Divide the numbers
dxdy=6y51
Take the derivative of both sides
dxd(dxdy)=dxd(6y51)
Calculate the derivative
dx2d2y=dxd(6y51)
Use differentiation rules
dx2d2y=61×dxd(y51)
Rewrite the expression in exponential form
dx2d2y=61×dxd(y−5)
Calculate the derivative
More Steps

Evaluate
dxd(y−5)
Use differentiation rules
dyd(y−5)×dxdy
Use dxdxn=nxn−1 to find derivative
−5y−6dxdy
dx2d2y=61(−5y−6dxdy)
Rewrite the expression
dx2d2y=61(−y65dxdy)
Calculate
dx2d2y=−6y65dxdy
Use equation dxdy=6y51 to substitute
dx2d2y=−6y65×6y51
Solution
More Steps

Calculate
−6y65×6y51
Multiply the terms
−6y66y55
Divide the terms
More Steps

Evaluate
6y66y55
Multiply by the reciprocal
6y55×6y61
Multiply the terms
6y5×6y65
Multiply the terms
36y115
−36y115
dx2d2y=−36y115
Show Solution
