Question
Function
Find the first partial derivative with respect to v
Find the first partial derivative with respect to a
∂v∂q=a1
Simplify
q=av
Find the first partial derivative by treating the variable a as a constant and differentiating with respect to v
∂v∂q=∂v∂(av)
Use differentiation rule ∂x∂(g(x)f(x))=(g(x))2∂x∂(f(x))×g(x)−f(x)×∂x∂(g(x))
∂v∂q=a2∂v∂(v)a−v×∂v∂(a)
Use ∂x∂xn=nxn−1 to find derivative
∂v∂q=a21×a−v×∂v∂(a)
Use ∂x∂(c)=0 to find derivative
∂v∂q=a21×a−v×0
Any expression multiplied by 1 remains the same
∂v∂q=a2a−v×0
Any expression multiplied by 0 equals 0
∂v∂q=a2a−0
Removing 0 doesn't change the value,so remove it from the expression
∂v∂q=a2a
Solution
More Steps

Evaluate
a2a
Use the product rule aman=an−m to simplify the expression
a2−11
Reduce the fraction
a1
∂v∂q=a1
Show Solution

Solve the equation
Solve for a
Solve for v
a=qv
Evaluate
q=av
Swap the sides of the equation
av=q
Cross multiply
v=aq
Simplify the equation
v=qa
Swap the sides of the equation
qa=v
Divide both sides
qqa=qv
Solution
a=qv
Show Solution
