What is (\partial}{\partial x}(\frac{sin(x))/x) ?

The answer to (\partial}{\partial x}(\frac{sin(x))/x) is (xcos(x)-sin(x))/(x^2)

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(\partial}{\partial x}(\frac{sin(x))/x)

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{\partial}{\partial x} (x) = 1

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

Simplify

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

y^{^{''}} - 2 y^{^{'}} + 10 y = 0, y (0) = 4, y^{^{'}} (0) = 1

x \to - 9 - lim (x^{2} + \frac{3}{x + 9})

\frac{\partial}{\partial y} (\frac{- y}{2 x ^{2} + y ^{2}})

\int (3 z + z^{2}) sin (z) d z

\frac{x - x}{x ^{\frac{1}{5}}}

What is (\partial}{\partial x}(\frac{sin(x))/x) ?
The answer to (\partial}{\partial x}(\frac{sin(x))/x) is (xcos(x)-sin(x))/(x^2)