Question
Function
Find the first partial derivative with respect to t
Find the first partial derivative with respect to f
∂t∂λ=f1
Simplify
λ=ft
Find the first partial derivative by treating the variable f as a constant and differentiating with respect to t
∂t∂λ=∂t∂(ft)
Use differentiation rule ∂x∂(g(x)f(x))=(g(x))2∂x∂(f(x))×g(x)−f(x)×∂x∂(g(x))
∂t∂λ=f2∂t∂(t)f−t×∂t∂(f)
Use ∂x∂xn=nxn−1 to find derivative
∂t∂λ=f21×f−t×∂t∂(f)
Use ∂x∂(c)=0 to find derivative
∂t∂λ=f21×f−t×0
Any expression multiplied by 1 remains the same
∂t∂λ=f2f−t×0
Any expression multiplied by 0 equals 0
∂t∂λ=f2f−0
Removing 0 doesn't change the value,so remove it from the expression
∂t∂λ=f2f
Solution
More Steps

Evaluate
f2f
Use the product rule aman=an−m to simplify the expression
f2−11
Reduce the fraction
f1
∂t∂λ=f1
Show Solution

Solve the equation
Solve for f
Solve for t
f=λt
Evaluate
λ=ft
Swap the sides of the equation
ft=λ
Cross multiply
t=fλ
Simplify the equation
t=λf
Swap the sides of the equation
λf=t
Divide both sides
λλf=λt
Solution
f=λt
Show Solution
