What is the derivative of ln((3+e^x/(3-e^x))) ?

The derivative of ln((3+e^x/(3-e^x))) is (6e^x)/((e^x+3)(-e^x+3))

What is the first derivative of ln((3+e^x/(3-e^x))) ?

The first derivative of ln((3+e^x/(3-e^x))) is (6e^x)/((e^x+3)(-e^x+3))

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Popular >

\frac{d}{d x} (ln (\frac{3 + e ^{x}}{3 - e ^{x}}))

\frac{6 e ^{x}}{( e ^{x} + 3 ) ( - e ^{x} + 3 )}

Solution steps

\frac{d}{d x} (ln (\frac{3 + e ^{x}}{3 - e ^{x}}))

Apply the chain rule:

\frac{1}{\frac{3 + e ^{x}}{3 - e ^{x}}} \frac{d}{d x} (\frac{3 + e ^{x}}{3 - e ^{x}})

= \frac{1}{\frac{3 + e ^{x}}{3 - e ^{x}}} \frac{d}{d x} (\frac{3 + e ^{x}}{3 - e ^{x}})

\frac{d}{d x} (\frac{3 + e ^{x}}{3 - e ^{x}}) = \frac{6 e ^{x}}{( 3 - e ^{x} ) ^{2}}

= \frac{1}{\frac{3 + e ^{x}}{3 - e ^{x}}} \cdot \frac{6 e ^{x}}{( 3 - e ^{x} ) ^{2}}

Simplify

\frac{1}{\frac{3 + e ^{x}}{3 - e ^{x}}} \cdot \frac{6 e ^{x}}{( 3 - e ^{x} ) ^{2}} : \frac{6 e ^{x}}{( e ^{x} + 3 ) ( - e ^{x} + 3 )}

= \frac{6 e ^{x}}{( e ^{x} + 3 ) ( - e ^{x} + 3 )}

\frac{d}{d x} (a x^{4} + b x^{3} + c x^{2})

(3 x - 1)^{7} (2 x + 1)^{5}

\frac{d}{d y} (e^{2 y})

f (x) = x^{6} (x - 1)^{5}

\int (x^{4} - \frac{1}{2} x^{3} + \frac{1}{4} x - 2) d x

What is the derivative of ln((3+e^x/(3-e^x))) ?
The derivative of ln((3+e^x/(3-e^x))) is (6e^x)/((e^x+3)(-e^x+3))
What is the first derivative of ln((3+e^x/(3-e^x))) ?
The first derivative of ln((3+e^x/(3-e^x))) is (6e^x)/((e^x+3)(-e^x+3))