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I have a function $f(x)$ which I would like to have the derivative with respect to $x$. How can I get the derivative of the following function with respect to $x$?
$$f(x) = \log(1-z^{e^{y^{T}x}})$$
1 Answer
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By the chain rule applied multiple times (assuming $z$ is a constant, and not a function of $x$): $$f^\prime(x)=\dfrac{1}{1-z^{e^{y^Tx}}}\left(-z^{e^{y^Tx}}\ln z\right)\left(e^{y^Tx}\times \dfrac{\mathrm d}{\mathrm{d}x}\left(y^Tx\right)\right)$$
