Differentiating u ( λ λ , T ) with respect to λ λ and setting the derivative equal to zero gives: ∂ ∂ u ∂ ∂ λ λ = 2 h c 2 ( h c k T λ λ 7 e h c / λ λ k T ( e h c / λ λ k T − − 1 ) 2 − − 1 λ λ 6 5 e h c / λ λ k T − − 1 ) = 0 , which can be simplified to give: h c λ λ k T e h c / λ λ k T e h c / λ λ k T − − 1 − − 5 = 0.