# What is the derivative of # f(x) = x^5 * (x^2-3)^6#?

Here:

We may apply the product rule here:

So:

becomes:

Streamlining:

Here, the chain rule can be used:

becomes:

Simplifying the previous formula:

becomes:

Extending it:

And there it is, our response.

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To find the derivative of ( f(x) = x^5 \cdot (x^2-3)^6 ), apply the product rule and the chain rule. The derivative is:

[ f'(x) = 5x^4 \cdot (x^2-3)^6 + x^5 \cdot 6(x^2-3)^5 \cdot 2x ]

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