DERIVADA DE[tex]f(x) = x ^ {2} (x - 2) ^ {4} [ / tex]?

<img src="https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%28x%5E2%5Cleft%28x-2%5Cright%294%5Cright%29%3D4x%5Cleft%283x-4%5Cright%29" />

Sacamos la constante :

<img src="https://tex.z-dn.net/?f=%3D4%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%28x%5E2%5Cleft%28x-2%5Cright%29%5Cright%29" />

Aplicamos la regla del producto :

<img src="https://tex.z-dn.net/?f=%3D4%5Cleft%28%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%28x%5E2%5Cright%29%5Cleft%28x-2%5Cright%29%2B%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%28x-2%5Cright%29x%5E2%5Cright%29" />

Aplicamos la regla de la potencia :

<img src="https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%28x%5E2%5Cright%29" />

<img src="https://tex.z-dn.net/?f=%3D2x%5E%7B2-1%7D" /><img src="https://tex.z-dn.net/?f=%3D2x" />

Aplicamos la regla de la suma :

<img src="https://tex.z-dn.net/?f=%3D%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%28x%5Cright%29-%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%282%5Cright%29" />

<img src="https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%28x-2%5Cright%29" />

Aplicando la regla de la derivación :

<img src="https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%28x%5Cright%29%3D1" />

<img src="https://tex.z-dn.net/?f=%3D1" />

Juntamos términos :

[img = 10]

Simplificamos

[img = 11].