## Calculus, 10th Edition (Anton)

$\dfrac{d\omega}{d\lambda}=-\dfrac{b^2\lambda}{a^2\omega}$
In order to derivate this function you have to apply implicit differentation method. First, take the function to it's $f(\lambda)=0$ form $a^2\omega^2+b^2\lambda^2-1=0$ Then derivate the whole equation. Rember the put $\omega'$ every time you derivate $\omega$ $2a^2\omega \omega^2 + 2b^2\lambda=0$ Solve for a' and you have the answer $\omega' (2a^2\omega)=-2b^2\lambda$ $\omega '=-\dfrac{b^2\lambda}{a^2\omega}$