What is the derivative of-(6x/y) ?

The derivative of-(6x/y) is -(6(y-x\frac{dy)/(dx))}{y^2}

What is the first derivative of-(6x/y) ?

The first derivative of-(6x/y) is -(6(y-x\frac{dy)/(dx))}{y^2}

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\frac{d}{d x} (- \frac{6 x}{y})

- \frac{6 ( y - x \frac{d y}{d x} )}{y ^{2}}

Solution steps

\frac{d}{d x} (- \frac{6 x}{y})

Take the constant out:

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

= - 6 \frac{d}{d x} (\frac{x}{y})

Apply the Quotient Rule:

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

= - 6 \cdot \frac{\frac{d x}{d x} y - \frac{d y}{d x} x}{y ^{2}}

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

= - 6 \cdot \frac{1 \cdot y - \frac{d y}{d x} x}{y ^{2}}

Simplify

- 6 \cdot \frac{1 \cdot y - \frac{d y}{d x} x}{y ^{2}} : - \frac{6 ( y - x \frac{d y}{d x} )}{y ^{2}}

= - \frac{6 ( y - x \frac{d y}{d x} )}{y ^{2}}

\frac{9}{x}

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

\int x^{2} 1 0^{x^{3}} d x

n = 0 \sum \infty \frac{n 7 ^{n}}{n !}

\int_{0}^{\infty} 5 e^{- 5 x} d x

What is the derivative of-(6x/y) ?
The derivative of-(6x/y) is -(6(y-x\frac{dy)/(dx))}{y^2}
What is the first derivative of-(6x/y) ?
The first derivative of-(6x/y) is -(6(y-x\frac{dy)/(dx))}{y^2}