What is the derivative of f(x)= 1/(8-11e^x) ?

The derivative of f(x)= 1/(8-11e^x) is (11e^x)/((8-11e^x)^2)

What is the first derivative of f(x)= 1/(8-11e^x) ?

The first derivative of f(x)= 1/(8-11e^x) is (11e^x)/((8-11e^x)^2)

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derivative of

f (x) = \frac{1}{8 - 11 e ^{x}}

\frac{11 e ^{x}}{( 8 - 11 e ^{x} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{8 - 11 e ^{x}})

Apply exponent rule:

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

= \frac{d}{d x} ((8 - 11 e^{x})^{- 1})

Apply the chain rule:

- \frac{1}{( 8 - 11 e ^{x} ) ^{2}} \frac{d}{d x} (8 - 11 e^{x})

= - \frac{1}{( 8 - 11 e ^{x} ) ^{2}} \frac{d}{d x} (8 - 11 e^{x})

\frac{d}{d x} (8 - 11 e^{x}) = - 11 e^{x}

= - \frac{1}{( 8 - 11 e ^{x} ) ^{2}} (- 11 e^{x})

Simplify

- \frac{1}{( 8 - 11 e ^{x} ) ^{2}} (- 11 e^{x}) : \frac{11 e ^{x}}{( 8 - 11 e ^{x} ) ^{2}}

= \frac{11 e ^{x}}{( 8 - 11 e ^{x} ) ^{2}}

What is the derivative of f(x)= 1/(8-11e^x) ?
The derivative of f(x)= 1/(8-11e^x) is (11e^x)/((8-11e^x)^2)
What is the first derivative of f(x)= 1/(8-11e^x) ?
The first derivative of f(x)= 1/(8-11e^x) is (11e^x)/((8-11e^x)^2)