Question
Function
Find the first partial derivative with respect to n
Find the first partial derivative with respect to p
∂n∂σ=p−p2
Simplify
σ=np(1−p)
Find the first partial derivative by treating the variable p as a constant and differentiating with respect to n
∂n∂σ=∂n∂(np(1−p))
Use differentiation rule ∂x∂(f(x)×g(x))=∂x∂(f(x))×g(x)+f(x)×∂x∂(g(x))
∂n∂σ=∂n∂(np)(1−p)+np×∂n∂(1−p)
Evaluate
More Steps

Evaluate
∂n∂(np)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
p×∂n∂(n)
Use ∂x∂xn=nxn−1 to find derivative
p×1
Multiply the terms
p
∂n∂σ=p(1−p)+np×∂n∂(1−p)
Evaluate
∂n∂σ=p−p2+np×∂n∂(1−p)
Use ∂x∂(c)=0 to find derivative
∂n∂σ=p−p2+np×0
Evaluate
∂n∂σ=p−p2+0
Solution
∂n∂σ=p−p2
Show Solution

Solve the equation
Solve for σ
Solve for n
Solve for p
σ=np−np2
Evaluate
σ=np(1−p)
Solution
σ=np−np2
Show Solution
