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

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

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

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

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derivative of

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

f (x) = 3 (x)^{3} + cos (x)

\int sin^{2020} (d) x d x

\frac{d}{d x} (- sin (3 x) 3)

\int (2 x + 1)^{- 1} d x

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