Question
Function
Find the first partial derivative with respect to l
Find the first partial derivative with respect to n
∂l∂b=n
Simplify
b=ln−1
Find the first partial derivative by treating the variable n as a constant and differentiating with respect to l
∂l∂b=∂l∂(ln−1)
Use differentiation rule ∂x∂(f(x)±g(x))=∂x∂(f(x))±∂x∂(g(x))
∂l∂b=∂l∂(ln)−∂l∂(1)
Evaluate
More Steps

Evaluate
∂l∂(ln)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
n×∂l∂(l)
Use ∂x∂xn=nxn−1 to find derivative
n×1
Multiply the terms
n
∂l∂b=n−∂l∂(1)
Use ∂x∂(c)=0 to find derivative
∂l∂b=n−0
Solution
∂l∂b=n
Show Solution

Solve the equation
Solve for l
Solve for n
l=nb+1
Evaluate
b=ln−1
Rewrite the expression
b=nl−1
Swap the sides of the equation
nl−1=b
Move the constant to the right-hand side and change its sign
nl=b+1
Divide both sides
nnl=nb+1
Solution
l=nb+1
Show Solution
