Algebra
Calculus
Trigonometry
Matrix
Question
Solve the equation
y=0
Evaluate
ycos(x)=x×2y×2
Multiply
More Steps
Evaluate
x×2y×2
Multiply the terms
x×4y
Use the commutative property to reorder the terms
4xy
ycos(x)=4xy
Rewrite the expression
cos(x)×y=4xy
Add or subtract both sides
cos(x)×y−4xy=0
Collect like terms by calculating the sum or difference of their coefficients
(cos(x)−4x)y=0
Solution
y=0
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
ycos(x)=x×2y×2
Multiply
More Steps
Evaluate
x×2y×2
Multiply the terms
x×4y
Use the commutative property to reorder the terms
4xy
ycos(x)=4xy
To test if the graph of ycos(x)=4xy is symmetry with respect to the origin,substitute -x for x and -y for y
−ycos(−x)=4(−x)(−y)
Use cos(−t)=cos(t) to transform the expression
−ycos(x)=4(−x)(−y)
Evaluate
−ycos(x)=4xy
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=cos(x)−4x4y+ysin(x)
Calculate
ycos(x)=x2y2
Simplify the expression
ycos(x)=4xy
Take the derivative of both sides
dxd(ycos(x))=dxd(4xy)
Calculate the derivative
More Steps
Evaluate
dxd(ycos(x))
Use differentiation rules
dxd(y)×cos(x)+y×dxd(cos(x))
Evaluate the derivative
More Steps
Evaluate
dxd(y)
Use differentiation rules
dyd(y)×dxdy
Use dxdxn=nxn−1 to find derivative
dxdy
dxdy×cos(x)+y×dxd(cos(x))
Use dxd(cosx)=−sinx to find derivative
dxdy×cos(x)−ysin(x)
dxdy×cos(x)−ysin(x)=dxd(4xy)
Calculate the derivative
More Steps
Evaluate
dxd(4xy)
Use differentiation rules
dxd(4x)×y+4x×dxd(y)
Evaluate the derivative
More Steps
Evaluate
dxd(4x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
4×dxd(x)
Use dxdxn=nxn−1 to find derivative
4×1
Any expression multiplied by 1 remains the same
4
4y+4x×dxd(y)
Evaluate the derivative
More Steps
Evaluate
dxd(y)
Use differentiation rules
dyd(y)×dxdy
Use dxdxn=nxn−1 to find derivative
dxdy
4y+4xdxdy
dxdy×cos(x)−ysin(x)=4y+4xdxdy
Rewrite the expression
cos(x)dxdy−ysin(x)=4y+4xdxdy
Move the expression to the left side
cos(x)dxdy−ysin(x)−4xdxdy=4y
Move the expression to the right side
cos(x)dxdy−4xdxdy=4y+ysin(x)
Collect like terms by calculating the sum or difference of their coefficients
(cos(x)−4x)dxdy=4y+ysin(x)
Divide both sides
cos(x)−4x(cos(x)−4x)dxdy=cos(x)−4x4y+ysin(x)
Solution
dxdy=cos(x)−4x4y+ysin(x)
Show Solution