I am trying to implicitly differentiate the following function: λ = exp ⁡ [ ( α + s λ − s ) − 1 ] Can someone help me with this?

Question

I am trying to implicitly differentiate the following function:  λ  =  exp  ⁡      [                  (        α        +                  s                      λ            −            s                          )                    −        1              ]  Can someone help me with this?

Olivia Petersen · Accepted Answer

Before making the differentiation you may simplify the equation such as  ln  ⁡  (  λ  )  =  −            (        α  +      s          λ      −      s                  )        ln  ⁡  (  λ  )  =  −            (                  α      (      λ      −      s      )      +      s              λ      −      s                  )        (  s  −  λ  )  ln  ⁡  (  λ  )  =  α  (  λ  −  s  )  +  sNow you can differentiate as below  −  ln  ⁡  (  λ  )  d  λ  +            s      −      λ        λ    d  λ  =  (  λ  −  s  )  d  α  +  α  d  λ            (        α  +            s      −      λ        λ    −  ln  ⁡  (  λ  )            )        d  λ  =  (  λ  −  s  )  d  α  →            d      λ              d      α        =            (      λ      −      s      )              α      +                        s          −          λ                λ            −      ln      ⁡      (      λ      )

I am trying to implicitly differentiate the following function: lambda=exp[(alpha+(s)/(lambda−s))^(−1)] Can someone help me with this?

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