Questions: Find the derivative of g(x) = 1 / x^15 using the extended power rule.

Find the derivative of g(x) = 1 / x^15 using the extended power rule.
Transcript text: Find the derivative of $g(x)=\frac{1}{x^{15}}$ using the extended power rule.
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Solution

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Solution Steps

Step 1: Rewrite the function

Rewrite the function g(x) as _g(x) = x⁻¹⁵_. This allows us to apply the power rule directly.

Step 2: Apply the power rule

The power rule states that the derivative of xⁿ is nxⁿ⁻¹. Applying this to g(x), we get _g'(x) = -15x⁻¹⁶_.

Final Answer

g'(x) = -15/x¹⁶

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