Algebra
Calculus
Trigonometry
Matrix
Question
Solve the equation
Solve for x
Solve for y
x=0x=243y1x=−243y1
Evaluate
8yx=x5
Cross multiply
x=8yx5
Add or subtract both sides
x−8yx5=0
Factor the expression
x(1−8yx4)=0
Separate the equation into 2 possible cases
x=01−8yx4=0
Solve the equation
More Steps
Evaluate
1−8yx4=0
Move the constant to the right-hand side and change its sign
−8yx4=0−1
Removing 0 doesn't change the value,so remove it from the expression
−8yx4=−1
Divide both sides
−8y−8yx4=−8y−1
Divide the numbers
x4=−8y−1
Use b−a=−ba=−ba to rewrite the fraction
x4=8y1
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±48y1
Simplify the expression
More Steps
Evaluate
48y1
To take a root of a fraction,take the root of the numerator and denominator separately
48y41
Simplify the radical expression
48y1
Simplify the radical expression
423y1
Multiply by the Conjugate
423y×4(23y)31×4(23y)3
Calculate
23y1×4(23y)3
Calculate
23y4(23y)3
x=±23y4(23y)3
Separate the equation into 2 possible cases
x=23y4(23y)3x=−23y4(23y)3
Calculate
x=23y429yx=−23y4(23y)3
Calculate
x=23y429yx=−23y429y
x=0x=23y429yx=−23y429y
Simplify
x=0x=243y1x=−23y429y
Solution
x=0x=243y1x=−243y1
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
8yx=x5
To test if the graph of 8yx=x5 is symmetry with respect to the origin,substitute -x for x and -y for y
8−y−x=(−x)5
Evaluate
More Steps
Evaluate
8−y−x
Express with a positive exponent using a−n=an1
8y1−x
Multiply by the reciprocal
−x×8y
−x×8y=(−x)5
Evaluate
−x×8y=−x5
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=3xln(2)−5×8yx4+1
Calculate
8yx=x5
Take the derivative of both sides
dxd(8yx)=dxd(x5)
Calculate the derivative
More Steps
Evaluate
dxd(8yx)
Use differentiation rules
(8y)2dxd(x)×8y−x×dxd(8y)
Use dxdxn=nxn−1 to find derivative
(8y)21×8y−x×dxd(8y)
Calculate the derivative
(8y)21×8y−xdxdy×ln(8)×8y
Any expression multiplied by 1 remains the same
(8y)28y−xdxdy×ln(8)×8y
Use the commutative property to reorder the terms
(8y)28y−ln(8)×xdxdy×8y
Calculate
(8y)28y−3ln(2)×xdxdy×8y
Calculate
82y8y−3ln(2)×xdxdy×8y
Calculate
8y1−3ln(2)×xdxdy
8y1−3ln(2)×xdxdy=dxd(x5)
Use dxdxn=nxn−1 to find derivative
8y1−3ln(2)×xdxdy=5x4
Rewrite the expression
8y1−3xln(2)×dxdy=5x4
Cross multiply
1−3xln(2)×dxdy=8y×5x4
Simplify the equation
1−3xln(2)×dxdy=5×8yx4
Move the constant to the right side
−3xln(2)×dxdy=5×8yx4−1
Divide both sides
−3xln(2)−3xln(2)×dxdy=−3xln(2)5×8yx4−1
Divide the numbers
dxdy=−3xln(2)5×8yx4−1
Solution
More Steps
Evaluate
−3xln(2)5×8yx4−1
Use b−a=−ba=−ba to rewrite the fraction
−3xln(2)5×8yx4−1
Rewrite the expression
3xln(2)−5×8yx4+1
dxdy=3xln(2)−5×8yx4+1
Show Solution