Question
Function
Find the first partial derivative with respect to t
Find the first partial derivative with respect to p
∂t∂k=p1
Simplify
k=pt
Find the first partial derivative by treating the variable p as a constant and differentiating with respect to t
∂t∂k=∂t∂(pt)
Use differentiation rule ∂x∂(g(x)f(x))=(g(x))2∂x∂(f(x))×g(x)−f(x)×∂x∂(g(x))
∂t∂k=p2∂t∂(t)p−t×∂t∂(p)
Use ∂x∂xn=nxn−1 to find derivative
∂t∂k=p21×p−t×∂t∂(p)
Use ∂x∂(c)=0 to find derivative
∂t∂k=p21×p−t×0
Any expression multiplied by 1 remains the same
∂t∂k=p2p−t×0
Any expression multiplied by 0 equals 0
∂t∂k=p2p−0
Removing 0 doesn't change the value,so remove it from the expression
∂t∂k=p2p
Solution
More Steps

Evaluate
p2p
Use the product rule aman=an−m to simplify the expression
p2−11
Reduce the fraction
p1
∂t∂k=p1
Show Solution

Solve the equation
Solve for p
Solve for t
p=kt
Evaluate
k=pt
Swap the sides of the equation
pt=k
Cross multiply
t=pk
Simplify the equation
t=kp
Swap the sides of the equation
kp=t
Divide both sides
kkp=kt
Solution
p=kt
Show Solution
