Question
Solve the equation
Solve for x
Solve for y
x=13−7+y5
Evaluate
y5−13x=7
Move the expression to the right-hand side and change its sign
−13x=7−y5
Change the signs on both sides of the equation
13x=−7+y5
Divide both sides
1313x=13−7+y5
Solution
x=13−7+y5
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
y5−13x=7
To test if the graph of y5−13x=7 is symmetry with respect to the origin,substitute -x for x and -y for y
(−y)5−13(−x)=7
Evaluate
More Steps

Evaluate
(−y)5−13(−x)
Multiply the numbers
(−y)5−(−13x)
Rewrite the expression
(−y)5+13x
Rewrite the expression
−y5+13x
−y5+13x=7
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=5y413
Calculate
y5−13x=7
Take the derivative of both sides
dxd(y5−13x)=dxd(7)
Calculate the derivative
More Steps

Evaluate
dxd(y5−13x)
Use differentiation rules
dxd(y5)+dxd(−13x)
Evaluate the derivative
More Steps

Evaluate
dxd(y5)
Use differentiation rules
dyd(y5)×dxdy
Use dxdxn=nxn−1 to find derivative
5y4dxdy
5y4dxdy+dxd(−13x)
Evaluate the derivative
More Steps

Evaluate
dxd(−13x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
−13×dxd(x)
Use dxdxn=nxn−1 to find derivative
−13×1
Any expression multiplied by 1 remains the same
−13
5y4dxdy−13
5y4dxdy−13=dxd(7)
Calculate the derivative
5y4dxdy−13=0
Move the constant to the right-hand side and change its sign
5y4dxdy=0+13
Removing 0 doesn't change the value,so remove it from the expression
5y4dxdy=13
Divide both sides
5y45y4dxdy=5y413
Solution
dxdy=5y413
Show Solution

Find the second derivative
Find the second derivative with respect to x
Find the second derivative with respect to y
dx2d2y=−25y9676
Calculate
y5−13x=7
Take the derivative of both sides
dxd(y5−13x)=dxd(7)
Calculate the derivative
More Steps

Evaluate
dxd(y5−13x)
Use differentiation rules
dxd(y5)+dxd(−13x)
Evaluate the derivative
More Steps

Evaluate
dxd(y5)
Use differentiation rules
dyd(y5)×dxdy
Use dxdxn=nxn−1 to find derivative
5y4dxdy
5y4dxdy+dxd(−13x)
Evaluate the derivative
More Steps

Evaluate
dxd(−13x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
−13×dxd(x)
Use dxdxn=nxn−1 to find derivative
−13×1
Any expression multiplied by 1 remains the same
−13
5y4dxdy−13
5y4dxdy−13=dxd(7)
Calculate the derivative
5y4dxdy−13=0
Move the constant to the right-hand side and change its sign
5y4dxdy=0+13
Removing 0 doesn't change the value,so remove it from the expression
5y4dxdy=13
Divide both sides
5y45y4dxdy=5y413
Divide the numbers
dxdy=5y413
Take the derivative of both sides
dxd(dxdy)=dxd(5y413)
Calculate the derivative
dx2d2y=dxd(5y413)
Use differentiation rules
dx2d2y=513×dxd(y41)
Rewrite the expression in exponential form
dx2d2y=513×dxd(y−4)
Calculate the derivative
More Steps

Evaluate
dxd(y−4)
Use differentiation rules
dyd(y−4)×dxdy
Use dxdxn=nxn−1 to find derivative
−4y−5dxdy
dx2d2y=513(−4y−5dxdy)
Rewrite the expression
dx2d2y=513(−y54dxdy)
Calculate
dx2d2y=−5y552dxdy
Use equation dxdy=5y413 to substitute
dx2d2y=−5y552×5y413
Solution
More Steps

Calculate
−5y552×5y413
Multiply the terms
More Steps

Multiply the terms
52×5y413
Multiply the terms
5y452×13
Multiply the terms
5y4676
−5y55y4676
Divide the terms
More Steps

Evaluate
5y55y4676
Multiply by the reciprocal
5y4676×5y51
Multiply the terms
5y4×5y5676
Multiply the terms
25y9676
−25y9676
dx2d2y=−25y9676
Show Solution
