Algebra
Calculus
Trigonometry
Matrix
Question
x2y2=z
Solve the equation
Solve for x
Solve for y
Solve for z
x=∣y∣zx=−∣y∣z
Evaluate
x2y2=z
Rewrite the expression
y2x2=z
Divide both sides
y2y2x2=y2z
Divide the numbers
x2=y2z
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±y2z
Simplify the expression
More Steps
Evaluate
y2z
To take a root of a fraction,take the root of the numerator and denominator separately
y2z
Simplify the radical expression
∣y∣z
x=±∣y∣z
Solution
x=∣y∣zx=−∣y∣z
Show Solution
Find the partial derivative
Find ∂x∂z by differentiating the equation directly
Find ∂y∂z by differentiating the equation directly
∂x∂z=2xy2
Evaluate
x2y2=z
Find ∂x∂z by taking the derivative of both sides with respect to x
∂x∂(x2y2)=∂x∂(z)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
y2×∂x∂(x2)=∂x∂(z)
Use ∂x∂xn=nxn−1 to find derivative
y2×2x=∂x∂(z)
Multiply the terms
2xy2=∂x∂(z)
Find the derivative
2xy2=∂x∂z
Solution
∂x∂z=2xy2
Show Solution