What is the derivative of ln(sqrt((3x^4+2/(4x)))) ?

The derivative of ln(sqrt((3x^4+2/(4x)))) is (9x^4-2)/(2x(3x^4+2))

What is the first derivative of ln(sqrt((3x^4+2/(4x)))) ?

The first derivative of ln(sqrt((3x^4+2/(4x)))) is (9x^4-2)/(2x(3x^4+2))

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\frac{d}{d x} (ln (\frac{3 x ^{4} + 2}{4 x}))

\frac{9 x ^{4} - 2}{2 x ( 3 x ^{4} + 2 )}

Solution steps

\frac{d}{d x} (ln (\frac{3 x ^{4} + 2}{4 x}))

Simplify

ln (\frac{3 x ^{4} + 2}{4 x}) : ln (\frac{3 x ^{4} + 2}{2 x})

= \frac{d}{d x} (ln (\frac{3 x ^{4} + 2}{2 x}))

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{3 x ^{4} + 2}{2 x}) = \frac{9 x ^{4} - 2}{4 x x 3 x ^{4} + 2}

= \frac{1}{\frac{3 x ^{4} + 2}{2 x}} \cdot \frac{9 x ^{4} - 2}{4 x x 3 x ^{4} + 2}

Simplify

\frac{1}{\frac{3 x ^{4} + 2}{2 x}} \cdot \frac{9 x ^{4} - 2}{4 x x 3 x ^{4} + 2} : \frac{9 x ^{4} - 2}{2 x ( 3 x ^{4} + 2 )}

= \frac{9 x ^{4} - 2}{2 x ( 3 x ^{4} + 2 )}

\int \frac{cos ( x )}{x ^{2}} d x

6^{4 - x^{2}}

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

\frac{d y}{d x} = 4 e^{3 x - 4 y}

\frac{d}{d x} (\frac{6}{2 ^{x}})

What is the derivative of ln(sqrt((3x^4+2/(4x)))) ?
The derivative of ln(sqrt((3x^4+2/(4x)))) is (9x^4-2)/(2x(3x^4+2))
What is the first derivative of ln(sqrt((3x^4+2/(4x)))) ?
The first derivative of ln(sqrt((3x^4+2/(4x)))) is (9x^4-2)/(2x(3x^4+2))