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=6−x2y2
Find the first partial derivative by treating the variable y as a constant and differentiating with respect to x
∂x∂z=∂x∂(6−x2y2)
Use differentiation rule ∂x∂(f(x)±g(x))=∂x∂(f(x))±∂x∂(g(x))
∂x∂z=∂x∂(6)−∂x∂(x2y2)
Use ∂x∂(c)=0 to find derivative
∂x∂z=0−∂x∂(x2y2)
Evaluate
More Steps
Evaluate
∂x∂(x2y2)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
y2×∂x∂(x2)
Use ∂x∂xn=nxn−1 to find derivative
y2×2x
Multiply the terms
2xy2
∂x∂z=0−2xy2
Solution
∂x∂z=−2xy2
Show Solution
Solve the equation
Solve for x
Solve for y
x=∣y∣−z+6x=−∣y∣−z+6
Evaluate
z=6−x2y2
Rewrite the expression
z=6−y2x2
Swap the sides of the equation
6−y2x2=z
Move the constant to the right-hand side and change its sign
−y2x2=z−6
Divide both sides
−y2−y2x2=−y2z−6
Divide the numbers
x2=−y2z−6
Divide the numbers
More Steps
Evaluate
−y2z−6
Use b−a=−ba=−ba to rewrite the fraction
−y2z−6
Rewrite the expression
y2−z+6
x2=y2−z+6
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±y2−z+6
Simplify the expression
More Steps
Evaluate
y2−z+6
To take a root of a fraction,take the root of the numerator and denominator separately
y2−z+6
Simplify the radical expression
∣y∣−z+6
x=±∣y∣−z+6
Solution
x=∣y∣−z+6x=−∣y∣−z+6
Show Solution