Find the second derivative of y=$$ x^6 $$-2/$$ x^3 $$

To find the second derivative of the function $ y = x^6 - \frac{2}{x^3} $, we first find the first derivative $ y' $:

1. Differentiate $ y $:
   \[
   y' = \frac{d}{dx}(x^6) - \frac{d}{dx}\left(\frac{2}{x^3}\right) = 6x^5 + \frac{6}{x^4}
   \]

Next, we find the second derivative $ y'' $:

2. Differentiate $ y' $:
   \[
   y'' = \frac{d}{dx}(6x^5) + \frac{d}{dx}\left(\frac{6}{x^4}\right) = 30x^4 - \frac{24}{x^5}
   \]

Thus, the second derivative is:
\[
y'' = 30x^4 - \frac{24}{x^5}
\]

Would you like more details or have any questions? Here are some related questions:

1. How do you find the first derivative of a function?
2. What is the significance of the second derivative in calculus?
3. Can you explain the concept of implicit differentiation?
4. How does the second derivative relate to the concavity of a function?
5. What are some applications of derivatives in real life?

**Tip:** Always simplify your derivatives as much as possible to make further calculations easier.

Find the second derivative of y=x^6 - 2/x^3

Discover how to find the second derivative of the function y = x^6 - 2/x^3 with a comprehensive solution. This includes calculating the first and second derivatives step-by-step, relevant for students in Grades 11-12.

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