What is the derivative of 1/(7-6e^x) ?

The derivative of 1/(7-6e^x) is (6e^x)/((7-6e^x)^2)

What is the first derivative of 1/(7-6e^x) ?

The first derivative of 1/(7-6e^x) is (6e^x)/((7-6e^x)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

\frac{1}{7 - 6 e ^{x}}

\frac{6 e ^{x}}{( 7 - 6 e ^{x} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{7 - 6 e ^{x}})

Apply exponent rule:

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

= \frac{d}{d x} ((7 - 6 e^{x})^{- 1})

Apply the chain rule:

- \frac{1}{( 7 - 6 e ^{x} ) ^{2}} \frac{d}{d x} (7 - 6 e^{x})

= - \frac{1}{( 7 - 6 e ^{x} ) ^{2}} \frac{d}{d x} (7 - 6 e^{x})

\frac{d}{d x} (7 - 6 e^{x}) = - 6 e^{x}

= - \frac{1}{( 7 - 6 e ^{x} ) ^{2}} (- 6 e^{x})

Simplify

- \frac{1}{( 7 - 6 e ^{x} ) ^{2}} (- 6 e^{x}) : \frac{6 e ^{x}}{( 7 - 6 e ^{x} ) ^{2}}

= \frac{6 e ^{x}}{( 7 - 6 e ^{x} ) ^{2}}

What is the derivative of 1/(7-6e^x) ?
The derivative of 1/(7-6e^x) is (6e^x)/((7-6e^x)^2)
What is the first derivative of 1/(7-6e^x) ?
The first derivative of 1/(7-6e^x) is (6e^x)/((7-6e^x)^2)