Algebra
Calculus
Trigonometry
Matrix
Question
Function
Find the first partial derivative with respect to y
Find the first partial derivative with respect to z
∂y∂x=2yz2
Simplify
x=y2z2
Find the first partial derivative by treating the variable z as a constant and differentiating with respect to y
∂y∂x=∂y∂(y2z2)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
∂y∂x=z2×∂y∂(y2)
Use ∂x∂xn=nxn−1 to find derivative
∂y∂x=z2×2y
Solution
∂y∂x=2yz2
Show Solution
Solve the equation
Solve for y
Solve for z
y=∣z∣xy=−∣z∣x
Evaluate
x=y2z2
Rewrite the expression
x=z2y2
Swap the sides of the equation
z2y2=x
Divide both sides
z2z2y2=z2x
Divide the numbers
y2=z2x
Take the root of both sides of the equation and remember to use both positive and negative roots
y=±z2x
Simplify the expression
More Steps
Evaluate
z2x
To take a root of a fraction,take the root of the numerator and denominator separately
z2x
Simplify the radical expression
∣z∣x
y=±∣z∣x
Solution
y=∣z∣xy=−∣z∣x
Show Solution