Cuando se deriva f(x) = 2x ^ 3 utilizando la expresion de limites resolviendo el producto notable y reduciendo terminos semejantes resulta la expresion :a) lim h - - >0 x ^ 3 + 3xh - h ^ 3 - 5 - - - -?

SOLUCIÓN

Hola‼

Recordemos la definición de derivada <img src="https://tex.z-dn.net/?f=%5Cboxed%7B%5Cmathrm%7B%5Cboldsymbol%7Bf%20%27%28a%29%20%3D%5Clim_%7Bh%20%5Cto%200%7D%20%5Cfrac%7Bf%28a%2Bh%29-f%28a%29%7D%7Bh%7D%7D%7D%7D" />

Entonces en el problema <img src="https://tex.z-dn.net/?f=f%20%27%28x%29%20%3D%5Clim_%7Bh%20%5Cto%200%7D%20%5Cdfrac%7Bf%28x%2Bh%29-f%28x%29%7D%7Bh%7D%7D%5C%5C%5C%5C%5C%5Cf%20%27%28x%29%20%3D%5Clim_%7Bh%20%5Cto%200%7D%20%5Cdfrac%7B2%28x%2Bh%29%5E%7B3%7D-2x%5E%7B3%7D%7D%7Bh%7D%7D%5C%5C%5C%5C%5C%5Cf%20%27%28x%29%20%3D%5Clim_%7Bh%20%5Cto%200%7D%20%5Cdfrac%7B2%28x%5E%7B3%7D%20%2B%203x%5E%7B2%7Dh%2B3xh%5E%7B2%7D%2Bh%5E%7B3%7D%29-2x%5E%7B3%7D%7D%7Bh%7D%7D%5C%5C%5C%5C%5C%5Cf%20%27%28x%29%20%3D%5Clim_%7Bh%20%5Cto%200%7D%20%5Cdfrac%7B2x%5E%7B3%7D%20%2B%206x%5E%7B2%7Dh%2B6xh%5E%7B2%7D%2B2h%5E%7B3%7D-2x%5E%7B3%7D%7D%7Bh%7D%7D%5C%5C%5C%5C%5C%5C%5Cboxed%7B%5Cboldsymbol%7B%5Cmathrm%7Bf%20%27%28x%29%20%3D%5Clim_%7Bh%20%5Cto%200%7D%20%5Cdfrac%7B6x%5E%7B2%7Dh%2B6xh%5E%7B2%7D%2B2h%5E%7B3%7D%7D%7Bh%7D%7D%7D%7D%7D" />.