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 e^{- x} cos (6 x) d x

\frac{d y}{d x} = \frac{x}{y ( x ^{2} + 1 )}

(2010, 73.1), (2000, 71.3)

\int cos^{2} (y) d y

\frac{\partial}{\partial x} (x^{2} + x y - 10)

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}