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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

= \frac{1}{3} \frac{d}{d x} (\frac{y}{x})

Apply the Quotient Rule:

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

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

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

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

Simplify

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

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

\frac{d y}{d x} = - 2 y, y (0) = 3

\frac{d}{d x} ((3 x^{2} + ln (x)) \cdot (5 x^{3})^{x})

\int 7 sin^{5} (x) cos (x) d x

x \to \infty lim (\frac{3 x - 2}{6 x + 1})

\frac{d ^{2} y}{d t ^{2}}

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