Alternative Equation Formats

The equation on this page is available in multiple formats. Depending on your browser, some formats might not render correctly.

MathML

\begin{aligned} \frac{d x}{d θ} & = \sum_{k} \frac{d φ (u_{k})}{d θ} = \sum_{k} [- \frac{u_{k} e^{- θ u_{k}}}{1 - e^{- θ u_{k}}} + \frac{e^{- θ}}{1 - e^{θ}}] \\ = \sum_{k} [- \frac{u_{k}}{e^{θ u_{k}} - 1} + \frac{1}{e^{θ} - 1}] \end{aligned}

Math Rendered as SVG

Math as LaTeX Source

\begin{align*} \frac{dx}{d\theta } & =\sum _ k \frac{d\varphi \left( u_{k}\right) }{d\theta }=\sum _ k \left[ -\frac{u_ k e^{-\theta u_ k}}{1-e^{-\theta u_ k}}+\frac{e^{-\theta }}{1-e^{\theta }}\right] \\ & =\sum _ k \left[ -\frac{u_{k}}{e^{\theta u_{k}}-1}+\frac{1}{e^{\theta }-1}\right] \end{align*}