Scolon 3 "La Dervoda" Calcular las doribadas de las sig funciones matematieco obleniendo la regla baska realizando bs oporaciones funtamentako do manora de Aplical la regla de dorivadas. a) $$ F(x)=\frac{\frac{6}{7} x^{3}-11 x^{2}+2 x^{-3}}{6 x^{2}} $$

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Alright, I need to calculate the derivatives of the given mathematical functions using the basic operations and applying the derivative rules. The function provided is:

$$ F(x) = \frac{\frac{6}{7} x^{3} - 11 x^{2} + 2 x^{-3}}{6 x^{2}} $$

First, I'll simplify the expression to make differentiation easier. Let's rewrite the function:

$$ F(x) = \frac{6}{7} x^{3} \cdot \frac{1}{6 x^{2}} - 11 x^{2} \cdot \frac{1}{6 x^{2}} + 2 x^{-3} \cdot \frac{1}{6 x^{2}} $$

Simplifying each term:

1. $$ \frac{6}{7} x^{3} \cdot \frac{1}{6 x^{2}} = \frac{6}{7} \cdot \frac{1}{6} \cdot x^{3-2} = \frac{1}{7} x $$
2. $$ -11 x^{2} \cdot \frac{1}{6 x^{2}} = -\frac{11}{6} $$
3. $$ 2 x^{-3} \cdot \frac{1}{6 x^{2}} = \frac{2}{6} x^{-3-2} = \frac{1}{3} x^{-5} $$

So, the simplified function is:

$$ F(x) = \frac{1}{7} x - \frac{11}{6} + \frac{1}{3} x^{-5} $$

Now, I'll find the derivative of each term with respect to $$ x $$:

1. $$ \frac{d}{dx} \left( \frac{1}{7} x \right) = \frac{1}{7} $$
2. $$ \frac{d}{dx} \left( -\frac{11}{6} \right) = 0 $$ (since it's a constant)
3. $$ \frac{d}{dx} \left( \frac{1}{3} x^{-5} \right) = \frac{1}{3} \cdot (-5) x^{-6} = -\frac{5}{3} x^{-6} $$

Combining these derivatives, the derivative of $$ F(x) $$ is:

$$ F'(x) = \frac{1}{7} - \frac{5}{3} x^{-6} $$

To express this in a more standard form, I'll write $$ x^{-6} $$ as $$ \frac{1}{x^{6}} $$:

$$ F'(x) = \frac{1}{7} - \frac{5}{3x^{6}} $$

Alternatively, combining the terms over a common denominator:

$$ F'(x) = \frac{3x^{6} - 35}{21x^{6}} $$

This is the derivative of the given function using basic differentiation rules.

La derivada de la función $$ F(x) = \frac{\frac{6}{7} x^{3} - 11 x^{2} + 2 x^{-3}}{6 x^{2}} $$ es: $$ F'(x) = \frac{1}{7} - \frac{5}{3x^{6}} $$ O también se puede expresar como: $$ F'(x) = \frac{3x^{6} - 35}{21x^{6}} $$

Scolon 3
“La Dervoda”
Calcular las doribadas de las sig funciones matematieco obleniendo la regla baska realizando bs oporaciones funtamentako do manora de Aplical la regla de dorivadas.
a)

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Scolon 3 “La Dervoda” Calcular las doribadas de las sig funciones matematieco obleniendo la regla baska realizando bs oporaciones funtamentako do manora de Aplical la regla de dorivadas. a)