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Popular >

Find the Derivative - d/dx (sin(x))/x

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

Popular Examples

Find dy/dx y=sec(x)

\frac{d y}{d x} y = sec (x)

Find the Derivative - d/dx 1/( natural log of x)derivative of

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

Find the Derivative - d/dx natural log of 2 derivative of

\frac{d}{d x} (ln (2))

Find the Derivative - d/dx natural log of 3 derivative of

\frac{d}{d x} (ln (3))

Find the Derivative - d/dx natural log of (x)^2 derivative of

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

Frequently Asked Questions (FAQ)

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