What is the derivative of 1/(x+ke^x) ?

The derivative of 1/(x+ke^x) is -(1+ke^x)/((x+ke^x)^2)

What is the first derivative of 1/(x+ke^x) ?

The first derivative of 1/(x+ke^x) is -(1+ke^x)/((x+ke^x)^2)

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derivative of

\frac{1}{x + k e ^{x}}

- \frac{1 + k e ^{x}}{( x + k e ^{x} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{x + k e ^{x}})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= \frac{d}{d x} ((x + k e^{x})^{- 1})

Apply the chain rule:

- \frac{1}{( x + k e ^{x} ) ^{2}} \frac{d}{d x} (x + k e^{x})

= - \frac{1}{( x + k e ^{x} ) ^{2}} \frac{d}{d x} (x + k e^{x})

\frac{d}{d x} (x + k e^{x}) = 1 + k e^{x}

= - \frac{1}{( x + k e ^{x} ) ^{2}} (1 + k e^{x})

Simplify

- \frac{1}{( x + k e ^{x} ) ^{2}} (1 + k e^{x}) : - \frac{1 + k e ^{x}}{( x + k e ^{x} ) ^{2}}

= - \frac{1 + k e ^{x}}{( x + k e ^{x} ) ^{2}}

\frac{d}{d x} (0.5)

cos (y)

\int 4 sin (2 t) d t

\frac{\partial}{\partial y} (tan (x) y)

\frac{d}{d x} ((arcsin (x))^{3})

What is the derivative of 1/(x+ke^x) ?
The derivative of 1/(x+ke^x) is -(1+ke^x)/((x+ke^x)^2)
What is the first derivative of 1/(x+ke^x) ?
The first derivative of 1/(x+ke^x) is -(1+ke^x)/((x+ke^x)^2)