What is the derivative of (9x)/(9x-5) ?

The derivative of (9x)/(9x-5) is -(45)/((9x-5)^2)

What is the first derivative of (9x)/(9x-5) ?

The first derivative of (9x)/(9x-5) is -(45)/((9x-5)^2)

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derivative of

\frac{9 x}{9 x - 5}

- \frac{45}{( 9 x - 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{9 x}{9 x - 5})

Take the constant out:

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

= 9 \frac{d}{d x} (\frac{x}{9 x - 5})

Apply the Quotient Rule:

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

= 9 \cdot \frac{\frac{d x}{d x} ( 9 x - 5 ) - \frac{d}{d x} ( 9 x - 5 ) x}{( 9 x - 5 ) ^{2}}

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

\frac{d}{d x} (9 x - 5) = 9

= 9 \cdot \frac{1 \cdot ( 9 x - 5 ) - 9 x}{( 9 x - 5 ) ^{2}}

Simplify

9 \cdot \frac{1 \cdot ( 9 x - 5 ) - 9 x}{( 9 x - 5 ) ^{2}} : - \frac{45}{( 9 x - 5 ) ^{2}}

= - \frac{45}{( 9 x - 5 ) ^{2}}

(y + 4) \cdot y^{^{'}} = 2 x y + 4 y

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

(2 x + y e^{\frac{y}{x}}) d x - x e^{\frac{y}{x}} d y = 0

\frac{d}{d x} (ln (\frac{cos ( x )}{x}))

\frac{d}{d x} ((4 x + 5 x^{2})^{4})

What is the derivative of (9x)/(9x-5) ?
The derivative of (9x)/(9x-5) is -(45)/((9x-5)^2)
What is the first derivative of (9x)/(9x-5) ?
The first derivative of (9x)/(9x-5) is -(45)/((9x-5)^2)