Algebra
Calculus
Trigonometry
Matrix
Question
Function
Find the first partial derivative with respect to x
Find the first partial derivative with respect to z
∂x∂y=2xz2
Simplify
y=x2z2
Find the first partial derivative by treating the variable z as a constant and differentiating with respect to x
∂x∂y=∂x∂(x2z2)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
∂x∂y=z2×∂x∂(x2)
Use ∂x∂xn=nxn−1 to find derivative
∂x∂y=z2×2x
Solution
∂x∂y=2xz2
Show Solution
Solve the equation
Solve for x
Solve for z
x=∣z∣yx=−∣z∣y
Evaluate
y=x2z2
Rewrite the expression
y=z2x2
Swap the sides of the equation
z2x2=y
Divide both sides
z2z2x2=z2y
Divide the numbers
x2=z2y
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±z2y
Simplify the expression
More Steps
Evaluate
z2y
To take a root of a fraction,take the root of the numerator and denominator separately
z2y
Simplify the radical expression
∣z∣y
x=±∣z∣y
Solution
x=∣z∣yx=−∣z∣y
Show Solution