Question
Function
Find the first partial derivative with respect to l
Find the first partial derivative with respect to w
∂l∂p=2
Simplify
p=2l+2w
Find the first partial derivative by treating the variable w as a constant and differentiating with respect to l
∂l∂p=∂l∂(2l+2w)
Use differentiation rule ∂x∂(f(x)±g(x))=∂x∂(f(x))±∂x∂(g(x))
∂l∂p=∂l∂(2l)+∂l∂(2w)
Evaluate
More Steps

Evaluate
∂l∂(2l)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
2×∂l∂(l)
Use ∂x∂xn=nxn−1 to find derivative
2×1
Multiply the terms
2
∂l∂p=2+∂l∂(2w)
Use ∂x∂(c)=0 to find derivative
∂l∂p=2+0
Solution
∂l∂p=2
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Solve the equation
Solve for l
Solve for w
l=2p−2w
Evaluate
p=2l+2w
Swap the sides of the equation
2l+2w=p
Move the expression to the right-hand side and change its sign
2l=p−2w
Divide both sides
22l=2p−2w
Solution
l=2p−2w
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