Question
Function
Find the first partial derivative with respect to x
Find the first partial derivative with respect to y
∂x∂γ=−x2y
Simplify
γ=x−1y
Find the first partial derivative by treating the variable y as a constant and differentiating with respect to x
∂x∂γ=∂x∂(x−1y)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
∂x∂γ=y×∂x∂(x−1)
Use ∂x∂xn=nxn−1 to find derivative
∂x∂γ=y(−x−2)
Multiply the terms
∂x∂γ=−x−2y
Express with a positive exponent using a−n=an1
∂x∂γ=−x21×y
Solution
∂x∂γ=−x2y
Show Solution
Solve the equation
Solve for x
Solve for γ
Solve for y
x=γy
Evaluate
γ=xT×xxTy
Simplify
More Steps
Evaluate
xT×xxTy
Multiply the terms
xT×xyxT
Multiply the terms with the same base by adding their exponents
xT+1yxT
γ=xT+1yxT
Evaluate
γ=xT×xxTy
Simplify
More Steps
Evaluate
xT×xxTy
Dividing by an is the same as multiplying by a−n
xTyx−T×x−1
Multiply the terms with the same base by adding their exponents
xT−T−1y
Subtract the terms
More Steps
Evaluate
T−T−1
The sum of two opposites equals 0
0−1
Remove 0
−1
x−1y
γ=x−1y
Rewrite the expression
γ=yx−1
Swap the sides of the equation
yx−1=γ
Rewrite the expression
xy=γ
Cross multiply
y=xγ
Simplify the equation
y=γx
Swap the sides of the equation
γx=y
Divide both sides
γγx=γy
Solution
x=γy
Show Solution