Special Derivative Function

Question

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 $x$?

$$f(x) = \log\left(1-z^{e^{y^{T}x}}\right)$$

Just use a crap ton of chain rules... it's tedious but you should be able to do it. — , Apr 24 '14 at 01:53

score 2 · Accepted Answer · answered Apr 24 '14 at 01:53

By the chain rule applied multiple times (assuming $z$ is a constant, and not a function of $x$): $$f^\prime(x)=\dfrac{1}{1-z^{e^{y^Tx}}}\left(-z^{e^{y^Tx}}\ln z\right)\left(e^{y^Tx}\times \dfrac{\mathrm d}{\mathrm{d}x}\left(y^Tx\right)\right)$$

Special Derivative Function

1 Answers1