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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

Multiply fractions:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

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

\frac{1}{x ^{2} + x + 1}

x \to 3 lim (5 x^{3} - 3 x^{2} + x - 6)

\int e^{r t} d t

\int 2 x e^{x^{2} + y^{2}} d x

x \to 2 + lim (\frac{1}{x - 2} - \frac{1}{x - 2})

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