Question
Solve the equation
Solve for x
Solve for y
Solve for z
x=3∣y∣−54y−6zyx=−3∣y∣−54y−6zy
Evaluate
−6x2y−4z=36
Rewrite the expression
−6yx2−4z=36
Move the expression to the right-hand side and change its sign
−6yx2=36+4z
Divide both sides
−6y−6yx2=−6y36+4z
Divide the numbers
x2=−6y36+4z
Divide the numbers
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Evaluate
−6y36+4z
Rewrite the expression
−6y2(18+2z)
Cancel out the common factor 2
−3y18+2z
Use b−a=−ba=−ba to rewrite the fraction
−3y18+2z
x2=−3y18+2z
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±−3y18+2z
Simplify the expression
More Steps

Evaluate
−3y18+2z
Rewrite the expression
3y×3y(−18−2z)×3y
Calculate
More Steps

Evaluate
(−18−2z)×3y
Multiply the terms
(−54−6z)y
Apply the distributive property
−54y−6zy
3y×3y−54y−6zy
Calculate
9y2−54y−6zy
To take a root of a fraction,take the root of the numerator and denominator separately
9y2−54y−6zy
Simplify the radical expression
More Steps

Evaluate
9y2
Rewrite the expression
9×y2
Simplify the root
3∣y∣
3∣y∣−54y−6zy
x=±3∣y∣−54y−6zy
Solution
x=3∣y∣−54y−6zyx=−3∣y∣−54y−6zy
Show Solution

Find the partial derivative
Find ∂x∂z by differentiating the equation directly
Find ∂y∂z by differentiating the equation directly
∂x∂z=−3xy
Evaluate
−6x2y−4z=36
Find ∂x∂z by taking the derivative of both sides with respect to x
∂x∂(−6x2y−4z)=∂x∂(36)
Use differentiation rule ∂x∂(f(x)±g(x))=∂x∂(f(x))±∂x∂(g(x))
−∂x∂(6x2y)−∂x∂(4z)=∂x∂(36)
Evaluate
More Steps

Evaluate
∂x∂(6x2y)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
6y×∂x∂(x2)
Use ∂x∂xn=nxn−1 to find derivative
6y×2x
Multiply the terms
12xy
−12xy−∂x∂(4z)=∂x∂(36)
Evaluate
More Steps

Evaluate
∂x∂(4z)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
4×∂x∂(z)
Find the derivative
4∂x∂z
−12xy−4∂x∂z=∂x∂(36)
Find the partial derivative
−12xy−4∂x∂z=0
Move the expression to the right-hand side and change its sign
−4∂x∂z=0+12xy
Add the terms
−4∂x∂z=12xy
Change the signs on both sides of the equation
4∂x∂z=−12xy
Divide both sides
44∂x∂z=4−12xy
Divide the numbers
∂x∂z=4−12xy
Solution
More Steps

Evaluate
4−12xy
Reduce the numbers
1−3xy
Calculate
−3xy
∂x∂z=−3xy
Show Solution
