Derivada de la función f(x) = [(x - 2) / (x + 2)] resuelta con el metodo de los 4 pasos?

<img src="https://tex.z-dn.net/?f=%5Ctextup%7Bla%20expresi%5C%27on%20es%3A%7D%5C%5Cf%28x%29%3D%5Cfrac%7Bx-2%7D%7Bx%2B2%7D%5C%5C%5Ctextup%7BUsando%20la%20regla%20de%20los%204%20pasos%20se%20tiene%3A%7D%5C%5C%5Ctextup%7B1.-Incrementamos%20la%20funci%5C%27on%7D%5C%5Cf%27%28x%29%3Df%28x%2B%5CDelta%20x%29%3D%5Clim_%7B%5CDelta%20x%5Cto0%7D%5Cfrac%7Bf%28x%2B%5CDelta%20x%29-f%28x%29%7D%7B%5CDelta%20x%7D%3D%5Clim_%7B%5CDelta%20x%5Cto0%7D%5Cleft%5B%5Cfrac%7Bx%2B%5CDelta%20x-2%7D%7Bx%2B%5CDelta%20x%2B2%7D%5Cright%5D%5C%5C%5Ctextup%7B2.-Restamos%20la%20funci%5C%27on%20original%3A%7D%5C%5Cf%27%28x%29%3D%5Clim_%7B%5CDelta%20x%5Cto0%7D%5Cleft%5B%5Cfrac%7Bx%2B%5CDelta%20x-2%7D%7Bx%2B%5CDelta%20x%2B2%7D-%5Cfrac%7Bx-2%7D%7Bx%2B2%7D%5Cright%5D%5C%5Cf%27%28x%29%3D%5Clim_%7B%5CDelta%20x%5Cto%200%7D%5Cfrac%7B%28x%2B2%29%5Bx%2B%5CDelta%20x-2%5D-%5Bx%2B%5CDelta%20x%2B2%5D%28x-2%29%7D%7B%28x%2B2%29%5Bx%2B%5CDelta%20x%2B2%5D%7D%5C%5Cf%27%28x%29%3D%5Clim_%7B%5CDelta%20x%5Cto0%7D%5Cfrac%7Bx%5E%7B2%7D%2Bx%5CDelta%20x%2B2%5CDeltax-4-x%5E%7B2%7D-x%5CDelta%20x%2B2%5CDelta%20x%2B4%7D%7Bx%5E%7B2%7D%2Bx%5CDelta%20x%2B4x%2B2%5CDelta%20x%2B4%7D%5C%5Cf%27%28x%29%3D%5Clim_%7B%5CDelta%20x%5Cto0%7D%5Cfrac%7B4%5CDelta%20x%7D%7B%5CDelta%20x%28x%2B2%29%2Bx%5E%7B2%7D%2B4x%2B4%7D%5C%5Cf%27%28x%29%3D%5Clim_%7B%5CDelta%20x%5Cto0%7D%5Cfrac%7B4%5CDelta%20x%7D%7B%5CDelta%20x%28x%2B2%29%28x%2B2%29%5E%7B2%7D%7D%5C%5Cf%27%28x%29%3D%5Clim_%7B%5CDelta%20x%5Cto0%7D%5Cfrac%7B4%5CDelta%20x%7D%7B%5CDelta%20x%28x%2B2%29%5E%7B3%7D%7D%5C%5C%5Ctextup%7B3.-Dividiendo%20entre%3A%7D%5CDelta%20x%5C%2C%5Ctextup%7Bnos%20queda%3A%7D%5C%5Cf%27%28x%29%3D%5Clim_%7B%5CDelta%20x%5Cto0%7D%5Cfrac%7B4%7D%7B%28x%2B2%29%5E%7B3%7D%7D%5C%5C%5Ctextup%7B4.-Evaluando%20el%20l%5C%27imite%7D%5C%5Cf%27%28x%29%3D%5Clim_%7B%5CDelta%20x%5Cto0%7D%5Cfrac%7B4%7D%7B%28x%2B2%29%5E%7B3%7D%7D%5C%5Cf%27%28x%29%3D%5Cfrac%7B4%7D%7B%28x%2B2%29%5E%7B3%7D%7D" />

Saludos.