What is the derivative of (9+2x-4sqrt(x)/x) ?

The derivative of (9+2x-4sqrt(x)/x) is (2sqrt(x)-9)/(x^2)

What is the first derivative of (9+2x-4sqrt(x)/x) ?

The first derivative of (9+2x-4sqrt(x)/x) is (2sqrt(x)-9)/(x^2)

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\frac{d}{d x} (\frac{9 + 2 x - 4 x}{x})

\frac{2 x - 9}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{9 + 2 x - 4 x}{x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 9 + 2 x - 4 x ) x - \frac{d x}{d x} ( 9 + 2 x - 4 x )}{x ^{2}}

\frac{d}{d x} (9 + 2 x - 4 x) = - \frac{2}{x} + 2

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

= \frac{( - \frac{2}{x} + 2 ) x - 1 \cdot ( 9 + 2 x - 4 x )}{x ^{2}}

Simplify

\frac{( - \frac{2}{x} + 2 ) x - 1 \cdot ( 9 + 2 x - 4 x )}{x ^{2}} : \frac{2 x - 9}{x ^{2}}

= \frac{2 x - 9}{x ^{2}}

\int 5 x e^{- 5 x} d x

\int (\frac{y}{1 + y ^{2}}) d y

f (x) = 12 sin (\frac{π t}{4})

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

\int \frac{x + 1}{x ^{2} - x} d x

What is the derivative of (9+2x-4sqrt(x)/x) ?
The derivative of (9+2x-4sqrt(x)/x) is (2sqrt(x)-9)/(x^2)
What is the first derivative of (9+2x-4sqrt(x)/x) ?
The first derivative of (9+2x-4sqrt(x)/x) is (2sqrt(x)-9)/(x^2)