What is the derivative of (sin(y)/x) ?

The derivative of (sin(y)/x) is (xcos(y)\frac{dy)/(dx)-sin(y)}{x^2}

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

The first derivative of (sin(y)/x) is (xcos(y)\frac{dy)/(dx)-sin(y)}{x^2}

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

y^{^{''}} + y^{^{'}} = tan (x)

\int (\frac{1 + x + x}{x}) d x

\int \frac{x}{2 1 + x} d x

x = - y, x = 2 - y^{2}

x \to 6 lim (g (x))

What is the derivative of (sin(y)/x) ?
The derivative of (sin(y)/x) is (xcos(y)\frac{dy)/(dx)-sin(y)}{x^2}
What is the first derivative of (sin(y)/x) ?
The first derivative of (sin(y)/x) is (xcos(y)\frac{dy)/(dx)-sin(y)}{x^2}