Find the derivative of the function. $$ y=x^{-7}+x^{-6}-6 $$ $$ y^{\prime}(x)=\square $$

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To find the derivative of the function $$ y = x^{-7} + x^{-6} - 6 $$, we'll differentiate each term separately with respect to $$ x $$.

1. **Differentiate $$ x^{-7} $$:**
   $$
   \frac{d}{dx} \left( x^{-7} \right) = -7x^{-8}
   $$

2. **Differentiate $$ x^{-6} $$:**
   $$
   \frac{d}{dx} \left( x^{-6} \right) = -6x^{-7}
   $$

3. **Differentiate the constant $$ -6 $$:**
   $$
   \frac{d}{dx} \left( -6 \right) = 0
   $$

Now, combine the derivatives of each term:
$$
y'(x) = -7x^{-8} -6x^{-7}
$$

You can also express the derivative with positive exponents in the denominator:
$$
y'(x) = -\frac{7}{x^8} - \frac{6}{x^7}
$$

**Final Answer:**
$$
y^{\prime}(x) = -7\,x^{-8} - 6\,x^{-7}
$$
The derivative of the function $$ y = x^{-7} + x^{-6} - 6 $$ is $$ y^{\prime}(x) = -7x^{-8} - 6x^{-7} $$.

Find the derivative of the function. \[ y=x^{-7}+x^{-6}-6 \] \( y^{\prime}(x)=\square \)

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