Derivative of a logarithm (chain rule)

solution-verification derivatives

\begin{eqnarray} \frac{\partial }{\partial \theta} \left[-y \ln\left(\frac{1}{1+e^{-\theta x}}\right)\right]&=&\frac{\partial }{\partial \theta} \left[y \ln\left(1+e^{-\theta x}\right)\right] \\ &=& -\frac{y x e^{- \theta x}}{1+e^{- \theta x}} \color{red}{\frac{e^{\theta x}}{e^{\theta x}}} \\ &=& -\frac{y x}{1 + e^{\color{red}{+}\theta x}} \end{eqnarray}


You are right and Mathematica is wrong !

Related

Green's Function within the the given "quarter-space"
Definition of diffeological space
Laurent expansion for sin(1/z)
Are these new series formulae for $\zeta(2)$?
Use row reductions to show $det(T)=0$
A set which is not isomorphic to it's proper subset is finite
In how many ways can four prizes be distributed to three persons if every person receives at least one prize?
When is a polyhedron uniquely determined by its projections?
What's so special about square root cancellation?
Doubt in Integration a function on a $k$ - cell.
Show, that the intersection of two manifolds $M, N \subset \mathbb{R}^n$ doesn't need to be a manifold [closed]
If this sequence of paths tend to a certain path $\gamma$, does the integrals along those paths tend to the integral along $\gamma$?