Question
Solve the equation
Solve for x
Solve for y
x=24y6−1
Evaluate
4y4×6y2−1=x
Multiply
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Evaluate
4y4×6y2
Multiply the terms
24y4×y2
Multiply the terms with the same base by adding their exponents
24y4+2
Add the numbers
24y6
24y6−1=x
Solution
x=24y6−1
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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
4y4×6y2−1=x
Multiply
More Steps

Evaluate
4y4×6y2
Multiply the terms
24y4×y2
Multiply the terms with the same base by adding their exponents
24y4+2
Add the numbers
24y6
24y6−1=x
To test if the graph of 24y6−1=x is symmetry with respect to the origin,substitute -x for x and -y for y
24(−y)6−1=−x
Evaluate
24y6−1=−x
Solution
Not symmetry with respect to the origin
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Find the first derivative
Find the derivative with respect to x
Find the derivative with respect to y
dxdy=144y51
Calculate
4y46y2−1=x
Simplify the expression
24y6−1=x
Take the derivative of both sides
dxd(24y6−1)=dxd(x)
Calculate the derivative
More Steps

Evaluate
dxd(24y6−1)
Use differentiation rules
dxd(24y6)+dxd(−1)
Evaluate the derivative
More Steps

Evaluate
dxd(24y6)
Use differentiation rules
dyd(24y6)×dxdy
Evaluate the derivative
144y5dxdy
144y5dxdy+dxd(−1)
Use dxd(c)=0 to find derivative
144y5dxdy+0
Evaluate
144y5dxdy
144y5dxdy=dxd(x)
Use dxdxn=nxn−1 to find derivative
144y5dxdy=1
Divide both sides
144y5144y5dxdy=144y51
Solution
dxdy=144y51
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Find the second derivative
Find the second derivative with respect to x
Find the second derivative with respect to y
dx2d2y=−20736y115
Calculate
4y46y2−1=x
Simplify the expression
24y6−1=x
Take the derivative of both sides
dxd(24y6−1)=dxd(x)
Calculate the derivative
More Steps

Evaluate
dxd(24y6−1)
Use differentiation rules
dxd(24y6)+dxd(−1)
Evaluate the derivative
More Steps

Evaluate
dxd(24y6)
Use differentiation rules
dyd(24y6)×dxdy
Evaluate the derivative
144y5dxdy
144y5dxdy+dxd(−1)
Use dxd(c)=0 to find derivative
144y5dxdy+0
Evaluate
144y5dxdy
144y5dxdy=dxd(x)
Use dxdxn=nxn−1 to find derivative
144y5dxdy=1
Divide both sides
144y5144y5dxdy=144y51
Divide the numbers
dxdy=144y51
Take the derivative of both sides
dxd(dxdy)=dxd(144y51)
Calculate the derivative
dx2d2y=dxd(144y51)
Use differentiation rules
dx2d2y=1441×dxd(y51)
Rewrite the expression in exponential form
dx2d2y=1441×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=1441(−5y−6dxdy)
Rewrite the expression
dx2d2y=1441(−y65dxdy)
Calculate
dx2d2y=−144y65dxdy
Use equation dxdy=144y51 to substitute
dx2d2y=−144y65×144y51
Solution
More Steps

Calculate
−144y65×144y51
Multiply the terms
−144y6144y55
Divide the terms
More Steps

Evaluate
144y6144y55
Multiply by the reciprocal
144y55×144y61
Multiply the terms
144y5×144y65
Multiply the terms
20736y115
−20736y115
dx2d2y=−20736y115
Show Solution
