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Popular >

derivative of ((sin(x))/x)

Solution

\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

derivative of 9tan(7x)

\frac{d}{d x} (9 tan (7 x))

inverse oflaplace (4e^{(-s)})/((s^2+4s+13))inverse laplace

\frac{4 e ^{(- s)}}{( s ^{2} + 4 s + 13 )}

integral of 1/(x^2-6x-13)

\int \frac{1}{x ^{2} - 6 x - 13} d x

y^'=0.0017y(1500-y)

y^{^{'}} = 0.0017 y (1500 - y)

integral of (sin(3x))/(cos(3x))

\int \frac{sin ( 3 x )}{cos ( 3 x )} d x

Frequently Asked Questions (FAQ)

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