What is the derivative of (3x/(2y)) ?

The derivative of (3x/(2y)) is (3(y-x\frac{dy)/(dx))}{2y^2}

What is the first derivative of (3x/(2y)) ?

The first derivative of (3x/(2y)) is (3(y-x\frac{dy)/(dx))}{2y^2}

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\frac{d}{d x} (\frac{3 x}{2 y})

\frac{3 ( y - x \frac{d y}{d x} )}{2 y ^{2}}

Solution steps

\frac{d}{d x} (\frac{3 x}{2 y})

Take the constant out:

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

= \frac{3}{2} \frac{d}{d x} (\frac{x}{y})

Apply the Quotient Rule:

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

= \frac{3}{2} \cdot \frac{\frac{d x}{d x} y - \frac{d y}{d x} x}{y ^{2}}

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

= \frac{3}{2} \cdot \frac{1 \cdot y - \frac{d y}{d x} x}{y ^{2}}

Simplify

\frac{3}{2} \cdot \frac{1 \cdot y - \frac{d y}{d x} x}{y ^{2}} : \frac{3 ( y - x \frac{d y}{d x} )}{2 y ^{2}}

= \frac{3 ( y - x \frac{d y}{d x} )}{2 y ^{2}}

\int x^{3} 1 + 9 x^{2} d x

\int 1 + 3 x^{2} d x

x \to 0 lim (\frac{e ^{x} + e ^{- x} - 2}{x sin ( x )})

\int \frac{1}{x ^{2} + 8 x + 65} d x

\int e^{11 x} d x

What is the derivative of (3x/(2y)) ?
The derivative of (3x/(2y)) is (3(y-x\frac{dy)/(dx))}{2y^2}
What is the first derivative of (3x/(2y)) ?
The first derivative of (3x/(2y)) is (3(y-x\frac{dy)/(dx))}{2y^2}