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

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

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

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

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\frac{d}{d 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}}

y = ln (3 x^{5})

\frac{d y}{d x} + 2 y = 2 e^{x}

\frac{d}{d x} (x^{2} 10 x - 3)

3 y^{^{''}} + 17 y^{^{'}} + 10 y = 0

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

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