Question
Function
Find the first partial derivative with respect to x
Find the first partial derivative with respect to a
∂x∂y=2
Evaluate
y=2x−1×a
Any expression multiplied by 1 remains the same
y=2x−a
Find the first partial derivative by treating the variable a as a constant and differentiating with respect to x
∂x∂y=∂x∂(2x−a)
Use differentiation rule ∂x∂(f(x)±g(x))=∂x∂(f(x))±∂x∂(g(x))
∂x∂y=∂x∂(2x)−∂x∂(a)
Evaluate
More Steps

Evaluate
∂x∂(2x)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
2×∂x∂(x)
Use ∂x∂xn=nxn−1 to find derivative
2×1
Multiply the terms
2
∂x∂y=2−∂x∂(a)
Use ∂x∂(c)=0 to find derivative
∂x∂y=2−0
Solution
∂x∂y=2
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Solve the equation
Solve for x
Solve for a
Solve for y
x=2y+a
Evaluate
y=2x−1×a
Any expression multiplied by 1 remains the same
y=2x−a
Swap the sides of the equation
2x−a=y
Move the expression to the right-hand side and change its sign
2x=y+a
Divide both sides
22x=2y+a
Solution
x=2y+a
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