What is the derivative of ln((3e^x/(2x^2))) ?

The derivative of ln((3e^x/(2x^2))) is (x-2)/x

What is the first derivative of ln((3e^x/(2x^2))) ?

The first derivative of ln((3e^x/(2x^2))) is (x-2)/x

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\frac{d}{d x} (ln (\frac{3 e ^{x}}{2 x ^{2}}))

\frac{x - 2}{x}

Solution steps

\frac{d}{d x} (ln (\frac{3 e ^{x}}{2 x ^{2}}))

Apply the chain rule:

\frac{1}{\frac{3 e ^{x}}{2 x ^{2}}} \frac{d}{d x} (\frac{3 e ^{x}}{2 x ^{2}})

= \frac{1}{\frac{3 e ^{x}}{2 x ^{2}}} \frac{d}{d x} (\frac{3 e ^{x}}{2 x ^{2}})

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

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

Simplify

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

= \frac{x - 2}{x}

What is the derivative of ln((3e^x/(2x^2))) ?
The derivative of ln((3e^x/(2x^2))) is (x-2)/x
What is the first derivative of ln((3e^x/(2x^2))) ?
The first derivative of ln((3e^x/(2x^2))) is (x-2)/x