What is the derivative of log_{3}((xsqrt(x-1)/2)) ?

The derivative of log_{3}((xsqrt(x-1)/2)) is (3x-2)/(2ln(3)x(x-1))

What is the first derivative of log_{3}((xsqrt(x-1)/2)) ?

The first derivative of log_{3}((xsqrt(x-1)/2)) is (3x-2)/(2ln(3)x(x-1))

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\frac{d}{d x} (lo g_{3} (\frac{x x - 1}{2}))

\frac{3 x - 2}{2 ln ( 3 ) x ( x - 1 )}

Solution steps

\frac{d}{d x} (lo g_{3} (\frac{x x - 1}{2}))

Apply log rule:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

= \frac{d}{d x} \frac{ln ( \frac{x x - 1}{2} )}{ln ( 3 )}

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{ln ( 3 )} \frac{d}{d x} (ln (\frac{x x - 1}{2}))

Apply the chain rule:

\frac{1}{\frac{x x - 1}{2}} \frac{d}{d x} (\frac{x x - 1}{2})

= \frac{1}{\frac{x x - 1}{2}} \frac{d}{d x} (\frac{x x - 1}{2})

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

= \frac{1}{ln ( 3 )} \cdot \frac{1}{\frac{x x - 1}{2}} \cdot \frac{3 x - 2}{4 x - 1}

Simplify

\frac{1}{ln ( 3 )} \cdot \frac{1}{\frac{x x - 1}{2}} \cdot \frac{3 x - 2}{4 x - 1} : \frac{3 x - 2}{2 ln ( 3 ) x ( x - 1 )}

= \frac{3 x - 2}{2 ln ( 3 ) x ( x - 1 )}

\int \frac{10}{x ^{2} x ^{2} + 9} d x

y = 565 + t (37 t^{0.6} - 103)

y^{^{''}} + 4 y^{^{'}} + 4 y = 3 x e^{- 2 x}

\frac{d q}{d t} = k q^{2}

f (x) = (3 x + 1)^{5}

What is the derivative of log_{3}((xsqrt(x-1)/2)) ?
The derivative of log_{3}((xsqrt(x-1)/2)) is (3x-2)/(2ln(3)x(x-1))
What is the first derivative of log_{3}((xsqrt(x-1)/2)) ?
The first derivative of log_{3}((xsqrt(x-1)/2)) is (3x-2)/(2ln(3)x(x-1))