What is the derivative of-x/(5y) ?

The derivative of-x/(5y) is -(y-x\frac{dy)/(dx)}{5y^2}

What is the first derivative of-x/(5y) ?

The first derivative of-x/(5y) is -(y-x\frac{dy)/(dx)}{5y^2}

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\frac{d}{d x} (- \frac{x}{5 y})

- \frac{y - x \frac{d y}{d x}}{5 y ^{2}}

Solution steps

\frac{d}{d x} (- \frac{x}{5 y})

Take the constant out:

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

= - \frac{1}{5} \frac{d}{d x} (\frac{x}{y})

Apply the Quotient Rule:

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

= - \frac{1}{5} \cdot \frac{\frac{d x}{d x} y - \frac{d y}{d x} x}{y ^{2}}

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

= - \frac{1}{5} \cdot \frac{1 \cdot y - \frac{d y}{d x} x}{y ^{2}}

Simplify

- \frac{1}{5} \cdot \frac{1 \cdot y - \frac{d y}{d x} x}{y ^{2}} : - \frac{y - x \frac{d y}{d x}}{5 y ^{2}}

= - \frac{y - x \frac{d y}{d x}}{5 y ^{2}}

n = 1 \sum \infty 7 ln (\frac{n}{n + 1})

\frac{\partial}{\partial x} (((- 5 x + 28))^{\frac{4}{3}})

\frac{\partial}{\partial x} (\frac{5 x + 4}{7 y + 1})

x \to 0 lim (- \frac{1}{x ^{3}})

sin (2 t)

What is the derivative of-x/(5y) ?
The derivative of-x/(5y) is -(y-x\frac{dy)/(dx)}{5y^2}
What is the first derivative of-x/(5y) ?
The first derivative of-x/(5y) is -(y-x\frac{dy)/(dx)}{5y^2}