Question
Solve the equation
Solve for x
Solve for y
Solve for z
x=yzx=−yz
Evaluate
x2=y2z2
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±y2z2
Simplify the expression
More Steps

Evaluate
y2z2
Rewrite the expression
y2×z2
Simplify the root
∣yz∣
x=±∣yz∣
Remove the absolute value bars
x=±yz
Solution
x=yzx=−yz
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Find the partial derivative
Find ∂x∂z by differentiating the equation directly
Find ∂y∂z by differentiating the equation directly
∂x∂z=y2zx
Evaluate
x2=y2z2
Find ∂x∂z by taking the derivative of both sides with respect to x
∂x∂(x2)=∂x∂(y2z2)
Use ∂x∂xn=nxn−1 to find derivative
2x=∂x∂(y2z2)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
2x=y2×∂x∂(z2)
Use the chain rule ∂x∂(f(g))=∂g∂(f(g))×∂x∂(g) where the g=z, to find the derivative
2x=y2×∂z∂(z2)∂x∂z
Find the derivative
2x=y2×2z∂x∂z
Use the commutative property to reorder the terms
2x=2y2z∂x∂z
Swap the sides of the equation
2y2z∂x∂z=2x
Divide both sides
2y2z2y2z∂x∂z=2y2z2x
Divide the numbers
∂x∂z=2y2z2x
Solution
∂x∂z=y2zx
Show Solution
