Question
Function
Evaluate the derivative
Find the domain
Find the x-intercept/zero
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y′=76x3
Evaluate
y=x2×19x2
Simplify
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Evaluate
x2×19x2
Multiply the terms with the same base by adding their exponents
x2+2×19
Add the numbers
x4×19
Use the commutative property to reorder the terms
19x4
y=19x4
Take the derivative of both sides
y′=dxd(19x4)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
y′=19×dxd(x4)
Use dxdxn=nxn−1 to find derivative
y′=19×4x3
Solution
y′=76x3
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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
y=x219x2
Simplify the expression
y=19x4
To test if the graph of y=19x4 is symmetry with respect to the origin,substitute -x for x and -y for y
−y=19(−x)4
Simplify
−y=19x4
Change the signs both sides
y=−19x4
Solution
Not symmetry with respect to the origin
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Solve the equation
Solve for x
Solve for y
x=1946859yx=−1946859y
Evaluate
y=x2×19x2
Simplify
More Steps

Evaluate
x2×19x2
Multiply the terms with the same base by adding their exponents
x2+2×19
Add the numbers
x4×19
Use the commutative property to reorder the terms
19x4
y=19x4
Swap the sides of the equation
19x4=y
Divide both sides
1919x4=19y
Divide the numbers
x4=19y
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±419y
Simplify the expression
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Evaluate
419y
To take a root of a fraction,take the root of the numerator and denominator separately
4194y
Multiply by the Conjugate
419×41934y×4193
Calculate
194y×4193
Calculate
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Evaluate
4y×4193
The product of roots with the same index is equal to the root of the product
4y×193
Calculate the product
4193y
194193y
Calculate
1946859y
x=±1946859y
Solution
x=1946859yx=−1946859y
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Rewrite the equation
r=0r=319cos(θ)×cos(θ)3sin(θ)
Evaluate
y=x2×19x2
Simplify
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Evaluate
x2×19x2
Multiply the terms with the same base by adding their exponents
x2+2×19
Add the numbers
x4×19
Use the commutative property to reorder the terms
19x4
y=19x4
Move the expression to the left side
y−19x4=0
To convert the equation to polar coordinates,substitute x for rcos(θ) and y for rsin(θ)
sin(θ)×r−19(cos(θ)×r)4=0
Factor the expression
−19cos4(θ)×r4+sin(θ)×r=0
Factor the expression
r(−19cos4(θ)×r3+sin(θ))=0
When the product of factors equals 0,at least one factor is 0
r=0−19cos4(θ)×r3+sin(θ)=0
Solution
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Factor the expression
−19cos4(θ)×r3+sin(θ)=0
Subtract the terms
−19cos4(θ)×r3+sin(θ)−sin(θ)=0−sin(θ)
Evaluate
−19cos4(θ)×r3=−sin(θ)
Divide the terms
r3=19cos4(θ)sin(θ)
Simplify the expression
More Steps

Evaluate
319cos4(θ)sin(θ)
To take a root of a fraction,take the root of the numerator and denominator separately
319cos4(θ)3sin(θ)
Simplify the radical expression
319cos(θ)×cos(θ)3sin(θ)
r=319cos(θ)×cos(θ)3sin(θ)
r=0r=319cos(θ)×cos(θ)3sin(θ)
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