What is the derivative of 1/(5-4e^x) ?

The derivative of 1/(5-4e^x) is (4e^x)/((5-4e^x)^2)

What is the first derivative of 1/(5-4e^x) ?

The first derivative of 1/(5-4e^x) is (4e^x)/((5-4e^x)^2)

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\frac{d}{d x} (\frac{1}{5 - 4 e ^{x}})

\frac{4 e ^{x}}{( 5 - 4 e ^{x} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{5 - 4 e ^{x}})

Apply exponent rule:

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

= \frac{d}{d x} ((5 - 4 e^{x})^{- 1})

Apply the chain rule:

- \frac{1}{( 5 - 4 e ^{x} ) ^{2}} \frac{d}{d x} (5 - 4 e^{x})

= - \frac{1}{( 5 - 4 e ^{x} ) ^{2}} \frac{d}{d x} (5 - 4 e^{x})

\frac{d}{d x} (5 - 4 e^{x}) = - 4 e^{x}

= - \frac{1}{( 5 - 4 e ^{x} ) ^{2}} (- 4 e^{x})

Simplify

- \frac{1}{( 5 - 4 e ^{x} ) ^{2}} (- 4 e^{x}) : \frac{4 e ^{x}}{( 5 - 4 e ^{x} ) ^{2}}

= \frac{4 e ^{x}}{( 5 - 4 e ^{x} ) ^{2}}

\int \frac{2}{x ^{4} - 1} d x

x \to 4 lim (9)

x \to 0 + lim (\frac{x}{1 + x})

x \to 0 lim (v ec t or)

x \to \infty lim (ln (4 x))

What is the derivative of 1/(5-4e^x) ?
The derivative of 1/(5-4e^x) is (4e^x)/((5-4e^x)^2)
What is the first derivative of 1/(5-4e^x) ?
The first derivative of 1/(5-4e^x) is (4e^x)/((5-4e^x)^2)