Solve operatorname{sig}(x)=1/1+e^-x

$$\operatorname { sig } ( x ) = \frac { 1 } { 1 + e ^ { - x } }$$

Solve for g

$$g=-\frac{ie^{x}}{sx\left(e^{x}+1\right)}$$

$$x\neq 0\text{ and }s\neq 0\text{ and }\nexists n_{2}\in \mathrm{Z}\text{ : }x=i\times 2\pi n_{2}+\pi i\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }x=-2\pi n_{1}i-\pi i$$

Steps for Solving Linear Equation

The equation is in standard form.

$$isxg=\frac{1}{\frac{1}{e^{x}}+1}$$

Divide both sides by isx.

$$\frac{isxg}{isx}=\frac{e^{x}}{\left(e^{x}+1\right)isx}$$

Dividing by isx undoes the multiplication by isx.

$$g=\frac{e^{x}}{\left(e^{x}+1\right)isx}$$

Divide \frac{e^{x}}{e^{x}+1} by isx.

$$g=-\frac{ie^{x}}{sx\left(e^{x}+1\right)}$$

Solve for s

$$s=-\frac{ie^{x}}{gx\left(e^{x}+1\right)}$$

$$x\neq 0\text{ and }g\neq 0\text{ and }\nexists n_{2}\in \mathrm{Z}\text{ : }x=i\times 2\pi n_{2}+\pi i\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }x=-2\pi n_{1}i-\pi i$$

Steps for Solving Linear Equation

The equation is in standard form.

$$igxs=\frac{1}{\frac{1}{e^{x}}+1}$$

Divide both sides by igx.

$$\frac{igxs}{igx}=\frac{e^{x}}{\left(e^{x}+1\right)igx}$$

Dividing by igx undoes the multiplication by igx.

$$s=\frac{e^{x}}{\left(e^{x}+1\right)igx}$$

Divide \frac{e^{x}}{e^{x}+1} by igx.

$$s=-\frac{ie^{x}}{gx\left(e^{x}+1\right)}$$