What is the derivative of 1/(7-10e^x) ?

The derivative of 1/(7-10e^x) is (10e^x)/((7-10e^x)^2)

What is the first derivative of 1/(7-10e^x) ?

The first derivative of 1/(7-10e^x) is (10e^x)/((7-10e^x)^2)

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derivative of

\frac{1}{7 - 10 e ^{x}}

\frac{10 e ^{x}}{( 7 - 10 e ^{x} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{7 - 10 e ^{x}})

Apply exponent rule:

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

= \frac{d}{d x} ((7 - 10 e^{x})^{- 1})

Apply the chain rule:

- \frac{1}{( 7 - 10 e ^{x} ) ^{2}} \frac{d}{d x} (7 - 10 e^{x})

= - \frac{1}{( 7 - 10 e ^{x} ) ^{2}} \frac{d}{d x} (7 - 10 e^{x})

\frac{d}{d x} (7 - 10 e^{x}) = - 10 e^{x}

= - \frac{1}{( 7 - 10 e ^{x} ) ^{2}} (- 10 e^{x})

Simplify

- \frac{1}{( 7 - 10 e ^{x} ) ^{2}} (- 10 e^{x}) : \frac{10 e ^{x}}{( 7 - 10 e ^{x} ) ^{2}}

= \frac{10 e ^{x}}{( 7 - 10 e ^{x} ) ^{2}}

\frac{d}{d x} (\frac{ln ( x + 1 )}{ln ( x - 1 )})

x^{2} e^{- 3 x}

ln (e^{x} + 1)

\int_{1}^{4} 3 x^{2} - \frac{1}{x} d x

\int_{0}^{x} sin (x) d x

What is the derivative of 1/(7-10e^x) ?
The derivative of 1/(7-10e^x) is (10e^x)/((7-10e^x)^2)
What is the first derivative of 1/(7-10e^x) ?
The first derivative of 1/(7-10e^x) is (10e^x)/((7-10e^x)^2)