Algebra
Calculus
Trigonometry
Matrix
Question
Solve the equation
Solve for x
Solve for y
Solve for z
x=∣y∣yz+y2x=−∣y∣yz+y2
Evaluate
xyx−y=z
Multiply the terms
x2y−y=z
Rewrite the expression
yx2−y=z
Move the expression to the right-hand side and change its sign
yx2=z+y
Divide both sides
yyx2=yz+y
Divide the numbers
x2=yz+y
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±yz+y
Simplify the expression
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Evaluate
yz+y
Rewrite the expression
y×y(z+y)y
Calculate
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Evaluate
(z+y)y
Apply the distributive property
zy+y×y
Use the commutative property to reorder the terms
yz+y×y
Multiply the terms
yz+y2
y×yyz+y2
Calculate
y2yz+y2
To take a root of a fraction,take the root of the numerator and denominator separately
y2yz+y2
Simplify the radical expression
∣y∣yz+y2
x=±∣y∣yz+y2
Solution
x=∣y∣yz+y2x=−∣y∣yz+y2
Show Solution
Find the partial derivative
Find ∂x∂z by differentiating the equation directly
Find ∂y∂z by differentiating the equation directly
∂x∂z=2xy
Evaluate
xyx−y=z
Multiply the terms
x2y−y=z
Find ∂x∂z by taking the derivative of both sides with respect to x
∂x∂(x2y−y)=∂x∂(z)
Use differentiation rule ∂x∂(f(x)±g(x))=∂x∂(f(x))±∂x∂(g(x))
∂x∂(x2y)−∂x∂(y)=∂x∂(z)
Evaluate
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Evaluate
∂x∂(x2y)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
y×∂x∂(x2)
Use ∂x∂xn=nxn−1 to find derivative
y×2x
Multiply the terms
2xy
2xy−∂x∂(y)=∂x∂(z)
Use ∂x∂(c)=0 to find derivative
2xy−0=∂x∂(z)
Removing 0 doesn't change the value,so remove it from the expression
2xy=∂x∂(z)
Find the derivative
2xy=∂x∂z
Solution
∂x∂z=2xy
Show Solution