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\question % workshop bank Ch. 3 -> esergel34
Let $f(x) = x^{7x}$.
Robin uses the fact that $\frac{d}{dx} x^n = n x^{n-1}$ and decides
$$
f'(x) = 7x \cdot x^{7x-1} = 7 x^{7x}
$$
Jaime uses the fact that $\frac{d}{dx} b^x = b^x \cdot \ln(b)$ together with the chain rule and concludes that
$$
f'(x) = x^{7x} \cdot 7\ln(x).
$$
What is the actual derivative of $f(x)$? If you did not agree with Robin and/or Jaime, explain where they went wrong.

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