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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

\frac{d x}{d x} = 1

= - \frac{\frac{c o s ( l n ( x ) )}{x} x - 1 \cdot sin ( ln ( x ) )}{x ^{2}}

Simplify

- \frac{\frac{c o s ( l n ( x ) )}{x} x - 1 \cdot sin ( ln ( x ) )}{x ^{2}} : - \frac{cos ( ln ( x ) ) - sin ( ln ( x ) )}{x ^{2}}

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

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