Question
Function
Find the first partial derivative with respect to f
Find the first partial derivative with respect to λ
∂f∂c=λ1
Simplify
c=λf
Find the first partial derivative by treating the variable λ as a constant and differentiating with respect to f
∂f∂c=∂f∂(λf)
Use differentiation rule ∂x∂(g(x)f(x))=(g(x))2∂x∂(f(x))×g(x)−f(x)×∂x∂(g(x))
∂f∂c=λ2∂f∂(f)λ−f×∂f∂(λ)
Use ∂x∂xn=nxn−1 to find derivative
∂f∂c=λ21×λ−f×∂f∂(λ)
Use ∂x∂(c)=0 to find derivative
∂f∂c=λ21×λ−f×0
Any expression multiplied by 1 remains the same
∂f∂c=λ2λ−f×0
Any expression multiplied by 0 equals 0
∂f∂c=λ2λ−0
Removing 0 doesn't change the value,so remove it from the expression
∂f∂c=λ2λ
Solution
More Steps

Evaluate
λ2λ
Use the product rule aman=an−m to simplify the expression
λ2−11
Reduce the fraction
λ1
∂f∂c=λ1
Show Solution

Solve the equation
Solve for λ
Solve for f
λ=cf
Evaluate
c=λf
Swap the sides of the equation
λf=c
Cross multiply
f=λc
Simplify the equation
f=cλ
Swap the sides of the equation
cλ=f
Divide both sides
ccλ=cf
Solution
λ=cf
Show Solution
