Question
Solve the equation
Solve for x
Solve for y
Solve for z
x=y53z2y4
Evaluate
4x5y−3z2×4=0
Multiply the terms
4x5y−12z2=0
Rewrite the expression
4yx5−12z2=0
Move the expression to the right-hand side and change its sign
4yx5=0+12z2
Add the terms
4yx5=12z2
Divide both sides
4y4yx5=4y12z2
Divide the numbers
x5=4y12z2
Cancel out the common factor 4
x5=y3z2
Take the 5-th root on both sides of the equation
5x5=5y3z2
Calculate
x=5y3z2
Solution
More Steps

Evaluate
5y3z2
To take a root of a fraction,take the root of the numerator and denominator separately
5y53z2
Multiply by the Conjugate
5y×5y453z2×5y4
Calculate
y53z2×5y4
The product of roots with the same index is equal to the root of the product
y53z2y4
x=y53z2y4
Show Solution

Find the partial derivative
Find ∂x∂z by differentiating the equation directly
Find ∂y∂z by differentiating the equation directly
∂x∂z=6z5x4y
Evaluate
4x5y−3z2×4=0
Multiply the terms
4x5y−12z2=0
Find ∂x∂z by taking the derivative of both sides with respect to x
∂x∂(4x5y−12z2)=∂x∂(0)
Use differentiation rule ∂x∂(f(x)±g(x))=∂x∂(f(x))±∂x∂(g(x))
∂x∂(4x5y)−∂x∂(12z2)=∂x∂(0)
Evaluate
More Steps

Evaluate
∂x∂(4x5y)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
4y×∂x∂(x5)
Use ∂x∂xn=nxn−1 to find derivative
4y×5x4
Multiply the terms
20x4y
20x4y−∂x∂(12z2)=∂x∂(0)
Evaluate
More Steps

Evaluate
∂x∂(12z2)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
12×∂x∂(z2)
Use the chain rule ∂x∂(f(g))=∂g∂(f(g))×∂x∂(g) where the g=z, to find the derivative
12×∂z∂(z2)∂x∂z
Find the derivative
12×2z∂x∂z
Multiply the terms
24z∂x∂z
20x4y−24z∂x∂z=∂x∂(0)
Find the partial derivative
20x4y−24z∂x∂z=0
Move the expression to the right-hand side and change its sign
−24z∂x∂z=0−20x4y
Removing 0 doesn't change the value,so remove it from the expression
−24z∂x∂z=−20x4y
Divide both sides
−24z−24z∂x∂z=−24z−20x4y
Divide the numbers
∂x∂z=−24z−20x4y
Solution
∂x∂z=6z5x4y
Show Solution
