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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

Simplify

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

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

x \to 7 lim ((x^{2} - 49) (\frac{( x - 7 )}{∣ x - 7 ∣}))

\frac{d}{d x} (6 x + x)

\int \frac{2}{x 9 - x ^{2}} d x

x \to 0 - lim (\frac{1}{0})

f (x) = \frac{( 10 x )}{x ^{2} - 6}, at x = 4

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