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by owalt
198 days ago
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No, it is correct. The integral is with respect to x, and the ordinary/partial derivatives are with respect to t. Written out fully, the derivative computation is d/dt (x^t - 1)/ln(x) = d/dt [exp(ln(x)t) - 1]/ln(x)
= ln(x)exp(ln(x)t)/ln(x)
= exp(ln(x)t)
= x^t. Edit: d/dt exp(ln(x)t) = ln(x)exp(ln(x)t) by the chain rule, while d/dt (1/ln(x)) = 0 since the expression is constant with respect to t. There are convergence considerations that were not discussed in the blog post, but the computations seem to be correct. |
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