What is the derivative of f(x)= 1/(5-2e^x) ?

The derivative of f(x)= 1/(5-2e^x) is (2e^x)/((5-2e^x)^2)

What is the first derivative of f(x)= 1/(5-2e^x) ?

The first derivative of f(x)= 1/(5-2e^x) is (2e^x)/((5-2e^x)^2)

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derivative of

f (x) = \frac{1}{5 - 2 e ^{x}}

\frac{2 e ^{x}}{( 5 - 2 e ^{x} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{5 - 2 e ^{x}})

Apply exponent rule:

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

= \frac{d}{d x} ((5 - 2 e^{x})^{- 1})

Apply the chain rule:

- \frac{1}{( 5 - 2 e ^{x} ) ^{2}} \frac{d}{d x} (5 - 2 e^{x})

= - \frac{1}{( 5 - 2 e ^{x} ) ^{2}} \frac{d}{d x} (5 - 2 e^{x})

\frac{d}{d x} (5 - 2 e^{x}) = - 2 e^{x}

= - \frac{1}{( 5 - 2 e ^{x} ) ^{2}} (- 2 e^{x})

Simplify

- \frac{1}{( 5 - 2 e ^{x} ) ^{2}} (- 2 e^{x}) : \frac{2 e ^{x}}{( 5 - 2 e ^{x} ) ^{2}}

= \frac{2 e ^{x}}{( 5 - 2 e ^{x} ) ^{2}}

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What is the derivative of f(x)= 1/(5-2e^x) ?
The derivative of f(x)= 1/(5-2e^x) is (2e^x)/((5-2e^x)^2)
What is the first derivative of f(x)= 1/(5-2e^x) ?
The first derivative of f(x)= 1/(5-2e^x) is (2e^x)/((5-2e^x)^2)