What is the derivative of (2y/x) ?

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

What is the first derivative of (2y/x) ?

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

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (\frac{y}{x})

Apply the Quotient Rule:

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

= 2 \cdot \frac{\frac{d y}{d x} x - \frac{d x}{d x} y}{x ^{2}}

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

= 2 \cdot \frac{\frac{d y}{d x} x - 1 \cdot y}{x ^{2}}

Simplify

2 \cdot \frac{\frac{d y}{d x} x - 1 \cdot y}{x ^{2}} : \frac{2 ( x \frac{d y}{d x} - y )}{x ^{2}}

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

\int 9 sin^{4} (x) cos^{2} (x) d x

d er i v a t i v e y = x^{2} e^{- 3 x}

\int \frac{s}{3 s ^{2} + 1} d s

d x = x x^{2} - 16 d y

\frac{d}{d x} (a r (x) cos (x))

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