Question
Function
Find the first partial derivative with respect to x
Find the first partial derivative with respect to a
∂x∂y=3
Simplify
y=3x−4a
Find the first partial derivative by treating the variable a as a constant and differentiating with respect to x
∂x∂y=∂x∂(3x−4a)
Use differentiation rule ∂x∂(f(x)±g(x))=∂x∂(f(x))±∂x∂(g(x))
∂x∂y=∂x∂(3x)−∂x∂(4a)
Evaluate
More Steps

Evaluate
∂x∂(3x)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
3×∂x∂(x)
Use ∂x∂xn=nxn−1 to find derivative
3×1
Multiply the terms
3
∂x∂y=3−∂x∂(4a)
Use ∂x∂(c)=0 to find derivative
∂x∂y=3−0
Solution
∂x∂y=3
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Solve the equation
Solve for x
Solve for a
x=3y+4a
Evaluate
y=3x−4a
Swap the sides of the equation
3x−4a=y
Move the expression to the right-hand side and change its sign
3x=y+4a
Divide both sides
33x=3y+4a
Solution
x=3y+4a
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