What is the derivative of (d/(dx(sin(x)))/x) ?

The derivative of (d/(dx(sin(x)))/x) is -(sin(x))/x

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

The first derivative of (d/(dx(sin(x)))/x) is -(sin(x))/x

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

\frac{d ^{2} x}{d x ^{2}} = 0

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

= \frac{( - sin ( x ) ) x - 0 \cdot cos ( x )}{x ^{2}}

Simplify

\frac{( - sin ( x ) ) x - 0 \cdot cos ( x )}{x ^{2}} : - \frac{sin ( x )}{x}

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

What is the derivative of (d/(dx(sin(x)))/x) ?
The derivative of (d/(dx(sin(x)))/x) is -(sin(x))/x
What is the first derivative of (d/(dx(sin(x)))/x) ?
The first derivative of (d/(dx(sin(x)))/x) is -(sin(x))/x