What is the derivative of f(x)=(1+x-4sqrt(x))/x ?

The derivative of f(x)=(1+x-4sqrt(x))/x is (2sqrt(x)-1)/(x^2)

What is the first derivative of f(x)=(1+x-4sqrt(x))/x ?

The first derivative of f(x)=(1+x-4sqrt(x))/x is (2sqrt(x)-1)/(x^2)

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derivative of

f (x) = \frac{1 + x - 4 x}{x}

\frac{2 x - 1}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{1 + 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} ( 1 + x - 4 x ) x - \frac{d x}{d x} ( 1 + x - 4 x )}{x ^{2}}

\frac{d}{d x} (1 + x - 4 x) = - \frac{2}{x} + 1

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

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

Simplify

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

= \frac{2 x - 1}{x ^{2}}

What is the derivative of f(x)=(1+x-4sqrt(x))/x ?
The derivative of f(x)=(1+x-4sqrt(x))/x is (2sqrt(x)-1)/(x^2)
What is the first derivative of f(x)=(1+x-4sqrt(x))/x ?
The first derivative of f(x)=(1+x-4sqrt(x))/x is (2sqrt(x)-1)/(x^2)