Question
x4×2(y−4)×2=25
Solve the equation
y=4x425+16x4
Evaluate
x4×2(y−4)×2=25
Multiply
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Evaluate
x4×2(y−4)×2
Multiply the terms
x4×4(y−4)
Use the commutative property to reorder the terms
4x4(y−4)
4x4(y−4)=25
Divide both sides
4x44x4(y−4)=4x425
Divide the numbers
y−4=4x425
Move the constant to the right side
y=4x425+4
Solution
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Evaluate
4x425+4
Reduce fractions to a common denominator
4x425+4x44×4x4
Write all numerators above the common denominator
4x425+4×4x4
Multiply the terms
4x425+16x4
y=4x425+16x4
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
x4×2(y−4)×2=25
Multiply
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Evaluate
x4×2(y−4)×2
Multiply the terms
x4×4(y−4)
Use the commutative property to reorder the terms
4x4(y−4)
4x4(y−4)=25
To test if the graph of 4x4(y−4)=25 is symmetry with respect to the origin,substitute -x for x and -y for y
4(−x)4(−y−4)=25
Evaluate
4x4(−y−4)=25
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=x−4y+16
Calculate
(x4)2(y−4)2=25
Simplify the expression
4x4(y−4)=25
Take the derivative of both sides
dxd(4x4(y−4))=dxd(25)
Calculate the derivative
More Steps

Evaluate
dxd(4x4(y−4))
Use differentiation rules
dxd(4)×x4(y−4)+4×dxd(x4)×(y−4)+4x4×dxd(y−4)
Use dxdxn=nxn−1 to find derivative
dxd(4)×x4(y−4)+16x3y−64x3+4x4×dxd(y−4)
Evaluate the derivative
More Steps

Evaluate
dxd(y−4)
Use differentiation rules
dxd(y)+dxd(−4)
Evaluate the derivative
dxdy+dxd(−4)
Use dxd(c)=0 to find derivative
dxdy+0
Evaluate
dxdy
dxd(4)×x4(y−4)+16x3y−64x3+4x4dxdy
Calculate
16x3y−64x3+4x4dxdy
16x3y−64x3+4x4dxdy=dxd(25)
Calculate the derivative
16x3y−64x3+4x4dxdy=0
Move the expression to the right-hand side and change its sign
4x4dxdy=0−(16x3y−64x3)
Subtract the terms
More Steps

Evaluate
0−(16x3y−64x3)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
0−16x3y+64x3
Removing 0 doesn't change the value,so remove it from the expression
−16x3y+64x3
4x4dxdy=−16x3y+64x3
Divide both sides
4x44x4dxdy=4x4−16x3y+64x3
Divide the numbers
dxdy=4x4−16x3y+64x3
Solution
More Steps

Evaluate
4x4−16x3y+64x3
Rewrite the expression
4x44(−4yx3+16x3)
Reduce the fraction
x4−4yx3+16x3
Rewrite the expression
x4x3(−4y+16)
Reduce the fraction
More Steps

Evaluate
x4x3
Use the product rule aman=an−m to simplify the expression
x4−31
Subtract the terms
x11
Simplify
x1
x−4y+16
dxdy=x−4y+16
Show Solution

Find the second derivative
Find the second derivative with respect to x
Find the second derivative with respect to y
dx2d2y=x220y−80
Calculate
(x4)2(y−4)2=25
Simplify the expression
4x4(y−4)=25
Take the derivative of both sides
dxd(4x4(y−4))=dxd(25)
Calculate the derivative
More Steps

Evaluate
dxd(4x4(y−4))
Use differentiation rules
dxd(4)×x4(y−4)+4×dxd(x4)×(y−4)+4x4×dxd(y−4)
Use dxdxn=nxn−1 to find derivative
dxd(4)×x4(y−4)+16x3y−64x3+4x4×dxd(y−4)
Evaluate the derivative
More Steps

Evaluate
dxd(y−4)
Use differentiation rules
dxd(y)+dxd(−4)
Evaluate the derivative
dxdy+dxd(−4)
Use dxd(c)=0 to find derivative
dxdy+0
Evaluate
dxdy
dxd(4)×x4(y−4)+16x3y−64x3+4x4dxdy
Calculate
16x3y−64x3+4x4dxdy
16x3y−64x3+4x4dxdy=dxd(25)
Calculate the derivative
16x3y−64x3+4x4dxdy=0
Move the expression to the right-hand side and change its sign
4x4dxdy=0−(16x3y−64x3)
Subtract the terms
More Steps

Evaluate
0−(16x3y−64x3)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
0−16x3y+64x3
Removing 0 doesn't change the value,so remove it from the expression
−16x3y+64x3
4x4dxdy=−16x3y+64x3
Divide both sides
4x44x4dxdy=4x4−16x3y+64x3
Divide the numbers
dxdy=4x4−16x3y+64x3
Divide the numbers
More Steps

Evaluate
4x4−16x3y+64x3
Rewrite the expression
4x44(−4yx3+16x3)
Reduce the fraction
x4−4yx3+16x3
Rewrite the expression
x4x3(−4y+16)
Reduce the fraction
More Steps

Evaluate
x4x3
Use the product rule aman=an−m to simplify the expression
x4−31
Subtract the terms
x11
Simplify
x1
x−4y+16
dxdy=x−4y+16
Take the derivative of both sides
dxd(dxdy)=dxd(x−4y+16)
Calculate the derivative
dx2d2y=dxd(x−4y+16)
Use differentiation rules
dx2d2y=x2dxd(−4y+16)×x−(−4y+16)×dxd(x)
Calculate the derivative
More Steps

Evaluate
dxd(−4y+16)
Use differentiation rules
dxd(−4y)+dxd(16)
Evaluate the derivative
−4dxdy+dxd(16)
Use dxd(c)=0 to find derivative
−4dxdy+0
Evaluate
−4dxdy
dx2d2y=x2−4dxdy×x−(−4y+16)×dxd(x)
Use dxdxn=nxn−1 to find derivative
dx2d2y=x2−4dxdy×x−(−4y+16)×1
Use the commutative property to reorder the terms
dx2d2y=x2−4xdxdy−(−4y+16)×1
Any expression multiplied by 1 remains the same
dx2d2y=x2−4xdxdy−(−4y+16)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
dx2d2y=x2−4xdxdy+4y−16
Use equation dxdy=x−4y+16 to substitute
dx2d2y=x2−4x×x−4y+16+4y−16
Solution
More Steps

Calculate
x2−4x×x−4y+16+4y−16
Cancel out the common factor x
x2−4(−4y+16)+4y−16
Calculate the sum or difference
More Steps

Evaluate
−4(−4y+16)+4y−16
Expand the expression
16y−64+4y−16
Add the terms
20y−64−16
Subtract the numbers
20y−80
x220y−80
dx2d2y=x220y−80
Show Solution
