What is the derivative of f(x)=(9+4x-8sqrt(x))/x ?

The derivative of f(x)=(9+4x-8sqrt(x))/x is (4sqrt(x)-9)/(x^2)

What is the first derivative of f(x)=(9+4x-8sqrt(x))/x ?

The first derivative of f(x)=(9+4x-8sqrt(x))/x is (4sqrt(x)-9)/(x^2)

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derivative of

f (x) = \frac{9 + 4 x - 8 x}{x}

\frac{4 x - 9}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{9 + 4 x - 8 x}{x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 9 + 4 x - 8 x ) x - \frac{d x}{d x} ( 9 + 4 x - 8 x )}{x ^{2}}

\frac{d}{d x} (9 + 4 x - 8 x) = - \frac{4}{x} + 4

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

= \frac{( - \frac{4}{x} + 4 ) x - 1 \cdot ( 9 + 4 x - 8 x )}{x ^{2}}

Simplify

\frac{( - \frac{4}{x} + 4 ) x - 1 \cdot ( 9 + 4 x - 8 x )}{x ^{2}} : \frac{4 x - 9}{x ^{2}}

= \frac{4 x - 9}{x ^{2}}

2 y = 5 x, y = 5, 2 y + 4 x = 9

\int \frac{1}{z ^{3} z ^{2} - 25} d z

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\int 18 sin^{2} (x) cos^{2} (x) d x

What is the derivative of f(x)=(9+4x-8sqrt(x))/x ?
The derivative of f(x)=(9+4x-8sqrt(x))/x is (4sqrt(x)-9)/(x^2)
What is the first derivative of f(x)=(9+4x-8sqrt(x))/x ?
The first derivative of f(x)=(9+4x-8sqrt(x))/x is (4sqrt(x)-9)/(x^2)