# How do I apply the implicit function theorem to find the derivative wrt to a parameter in this specific equation?

$λ^2=\frac{p(2-2p)}{(p^2+a)}$

$p=\frac{(2λ-2+λb)}{(2λ+4)(λ-1)}$

Where $a$ and $b$ are positive parameters. How can I find $∂p/∂a$ and $∂λ/∂a$ ?

A little background: this two equations are obtained from the first order conditions of a maximization problem. Thanks!

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The equations are easily solved for $a$ and $b$, so you can compute the matrix of partial derivatives of $(a,b)$ with respect to $(\lambda,p)$. Then use the fact that this is the inverse of the matrix of partial derivatives of $(\lambda,p)$ with respect to $(a,b)$.