Algebra
Calculus
Trigonometry
Matrix
Question
Function
Find the first partial derivative with respect to x
Find the first partial derivative with respect to y
∂x∂z=2xy2
Simplify
z=x2y2
Find the first partial derivative by treating the variable y as a constant and differentiating with respect to x
∂x∂z=∂x∂(x2y2)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
∂x∂z=y2×∂x∂(x2)
Use ∂x∂xn=nxn−1 to find derivative
∂x∂z=y2×2x
Solution
∂x∂z=2xy2
Show Solution
Solve the equation
Solve for x
Solve for y
x=∣y∣zx=−∣y∣z
Evaluate
z=x2y2
Rewrite the expression
z=y2x2
Swap the sides of the equation
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