Alternative Equation Formats

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MathML

\begin{array}{rcl} \frac{d Ψ_{m - 1}}{d θ} & = & \frac{d Ψ_{m - 1}}{d y} \frac{d y}{d θ} \\ = & \frac{d Ψ_{m - 1}}{d y} [\frac{d y}{d θ} + \frac{d y}{d x} \frac{d x}{d θ}] \\ = & \frac{d Ψ_{m - 1}}{d y} [\frac{e^{- x} e^{- θ}}{{[1 + e^{- x} (e^{- θ} - 1)]}^{2}} + \frac{e^{- x} (e^{- θ} - 1)}{{[1 + e^{- x} (e^{- θ} - 1)]}^{2}} \frac{d x}{d θ}] \end{array}

Math Rendered as SVG

Math as LaTeX Source

\begin{eqnarray*} \frac{d\Psi _{m-1}}{d\theta } & =& \frac{d\Psi _{m-1}}{dy}\frac{dy}{d\theta } \\ & =& \frac{d\Psi _{m-1}}{dy}\left[ \frac{dy}{d\theta }+\frac{dy}{dx}\frac{dx}{d\theta }\right] \\ & =& \frac{d\Psi _{m-1}}{dy}\left[ \frac{e^{-x}e^{-\theta }}{\left[ 1+e^{-x}\left( e^{-\theta }-1\right) \right] ^{2}}+\frac{e^{-x}\left( e^{-\theta }-1\right) }{\left[ 1+e^{-x}\left( e^{-\theta }-1\right) \right] ^{2}}\frac{dx}{d\theta }\right] \end{eqnarray*}