Question
Function
Find the first partial derivative with respect to f
Find the first partial derivative with respect to s
∂f∂p=s1
Simplify
p=sf
Find the first partial derivative by treating the variable s as a constant and differentiating with respect to f
∂f∂p=∂f∂(sf)
Use differentiation rule ∂x∂(g(x)f(x))=(g(x))2∂x∂(f(x))×g(x)−f(x)×∂x∂(g(x))
∂f∂p=s2∂f∂(f)s−f×∂f∂(s)
Use ∂x∂xn=nxn−1 to find derivative
∂f∂p=s21×s−f×∂f∂(s)
Use ∂x∂(c)=0 to find derivative
∂f∂p=s21×s−f×0
Any expression multiplied by 1 remains the same
∂f∂p=s2s−f×0
Any expression multiplied by 0 equals 0
∂f∂p=s2s−0
Removing 0 doesn't change the value,so remove it from the expression
∂f∂p=s2s
Solution
More Steps

Evaluate
s2s
Use the product rule aman=an−m to simplify the expression
s2−11
Reduce the fraction
s1
∂f∂p=s1
Show Solution

Solve the equation
Solve for f
Solve for s
f=ps
Evaluate
p=sf
Swap the sides of the equation
sf=p
Cross multiply
f=sp
Solution
f=ps
Show Solution
