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

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

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

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

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to 4 lim (\frac{1}{x + 2})

f (x) = (1 + x^{3})^{2020}

\frac{d}{d x} (2 x^{2} + 3)

y = ln (x + 9)

\frac{d}{d x} (4 x^{3} y)

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