What is the derivative of-(9x/y) ?

The derivative of-(9x/y) is -(9(y-x\frac{dy)/(dx))}{y^2}

What is the first derivative of-(9x/y) ?

The first derivative of-(9x/y) is -(9(y-x\frac{dy)/(dx))}{y^2}

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\frac{d}{d x} (- \frac{9 x}{y})

- \frac{9 ( y - x \frac{d y}{d x} )}{y ^{2}}

Solution steps

\frac{d}{d x} (- \frac{9 x}{y})

Take the constant out:

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

= - 9 \frac{d}{d x} (\frac{x}{y})

Apply the Quotient Rule:

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

= - 9 \cdot \frac{\frac{d x}{d x} y - \frac{d y}{d x} x}{y ^{2}}

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

= - 9 \cdot \frac{1 \cdot y - \frac{d y}{d x} x}{y ^{2}}

Simplify

- 9 \cdot \frac{1 \cdot y - \frac{d y}{d x} x}{y ^{2}} : - \frac{9 ( y - x \frac{d y}{d x} )}{y ^{2}}

= - \frac{9 ( y - x \frac{d y}{d x} )}{y ^{2}}

\frac{\partial}{\partial y} (x^{2} + y e^{x})

\frac{\partial}{\partial y} (ln (x - 6 y))

(1.85) (5.1)

\int x 4^{x^{2} + 5} d x

\frac{\partial}{\partial x} (4 x^{2} - x)

What is the derivative of-(9x/y) ?
The derivative of-(9x/y) is -(9(y-x\frac{dy)/(dx))}{y^2}
What is the first derivative of-(9x/y) ?
The first derivative of-(9x/y) is -(9(y-x\frac{dy)/(dx))}{y^2}