What is the derivative of (3x/(5y)) ?

The derivative of (3x/(5y)) is (3(y-x\frac{dy)/(dx))}{5y^2}

What is the first derivative of (3x/(5y)) ?

The first derivative of (3x/(5y)) is (3(y-x\frac{dy)/(dx))}{5y^2}

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\frac{d}{d x} (\frac{3 x}{5 y})

\frac{3 ( y - x \frac{d y}{d x} )}{5 y ^{2}}

Solution steps

\frac{d}{d x} (\frac{3 x}{5 y})

Take the constant out:

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

= \frac{3}{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{3}{5} \cdot \frac{\frac{d x}{d x} y - \frac{d y}{d x} x}{y ^{2}}

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

= \frac{3}{5} \cdot \frac{1 \cdot y - \frac{d y}{d x} x}{y ^{2}}

Simplify

\frac{3}{5} \cdot \frac{1 \cdot y - \frac{d y}{d x} x}{y ^{2}} : \frac{3 ( y - x \frac{d y}{d x} )}{5 y ^{2}}

= \frac{3 ( y - x \frac{d y}{d x} )}{5 y ^{2}}

\frac{m x}{b x + c}

\int (x + 5) 8 - x d x

\frac{\partial}{\partial x} (2 + 3 x y)

n = 0 \sum \infty (4 x^{2})^{n}

x \to π lim (9 sin (sin (x)))

What is the derivative of (3x/(5y)) ?
The derivative of (3x/(5y)) is (3(y-x\frac{dy)/(dx))}{5y^2}
What is the first derivative of (3x/(5y)) ?
The first derivative of (3x/(5y)) is (3(y-x\frac{dy)/(dx))}{5y^2}