What is the derivative of (sin(x)/(ln(x))) ?

The derivative of (sin(x)/(ln(x))) is (xcos(x)ln(x)-sin(x))/(xln^2(x))

What is the first derivative of (sin(x)/(ln(x))) ?

The first derivative of (sin(x)/(ln(x))) is (xcos(x)ln(x)-sin(x))/(xln^2(x))

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\frac{d}{d x} (\frac{sin ( x )}{ln ( x )})

\frac{x cos ( x ) ln ( x ) - sin ( x )}{x ln ^{2} ( x )}

Solution steps

\frac{d}{d x} (\frac{sin ( x )}{ln ( x )})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( sin ( x ) ) ln ( x ) - \frac{d}{d x} ( ln ( x ) ) sin ( x )}{( ln ( x ) ) ^{2}}

\frac{d}{d x} (sin (x)) = cos (x)

\frac{d}{d x} (ln (x)) = \frac{1}{x}

= \frac{cos ( x ) ln ( x ) - \frac{1}{x} sin ( x )}{( ln ( x ) ) ^{2}}

Simplify

\frac{cos ( x ) ln ( x ) - \frac{1}{x} sin ( x )}{ln ^{2} ( x )} : \frac{x cos ( x ) ln ( x ) - sin ( x )}{x ln ^{2} ( x )}

= \frac{x cos ( x ) ln ( x ) - sin ( x )}{x ln ^{2} ( x )}

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

y^{^{''}} - 8 y^{^{'}} + 16 = 0

x \to π lim ((π - x) cot (x))

(e^{- 1}) (sin (2 t))

e^{8 x} cos (11 x)

What is the derivative of (sin(x)/(ln(x))) ?
The derivative of (sin(x)/(ln(x))) is (xcos(x)ln(x)-sin(x))/(xln^2(x))
What is the first derivative of (sin(x)/(ln(x))) ?
The first derivative of (sin(x)/(ln(x))) is (xcos(x)ln(x)-sin(x))/(xln^2(x))