Question
Function
Find the first partial derivative with respect to q
Find the first partial derivative with respect to r
∂q∂v=r1
Simplify
v=rq
Find the first partial derivative by treating the variable r as a constant and differentiating with respect to q
∂q∂v=∂q∂(rq)
Use differentiation rule ∂x∂(g(x)f(x))=(g(x))2∂x∂(f(x))×g(x)−f(x)×∂x∂(g(x))
∂q∂v=r2∂q∂(q)r−q×∂q∂(r)
Use ∂x∂xn=nxn−1 to find derivative
∂q∂v=r21×r−q×∂q∂(r)
Use ∂x∂(c)=0 to find derivative
∂q∂v=r21×r−q×0
Any expression multiplied by 1 remains the same
∂q∂v=r2r−q×0
Any expression multiplied by 0 equals 0
∂q∂v=r2r−0
Removing 0 doesn't change the value,so remove it from the expression
∂q∂v=r2r
Solution
More Steps

Evaluate
r2r
Use the product rule aman=an−m to simplify the expression
r2−11
Reduce the fraction
r1
∂q∂v=r1
Show Solution

Solve the equation
Solve for q
Solve for r
q=rv
Evaluate
v=rq
Swap the sides of the equation
rq=v
Solution
q=rv
Show Solution
