What is the derivative of (3+5x-8sqrt(x)/x) ?

The derivative of (3+5x-8sqrt(x)/x) is (4sqrt(x)-3)/(x^2)

What is the first derivative of (3+5x-8sqrt(x)/x) ?

The first derivative of (3+5x-8sqrt(x)/x) is (4sqrt(x)-3)/(x^2)

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\frac{d}{d x} (\frac{3 + 5 x - 8 x}{x})

\frac{4 x - 3}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{3 + 5 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} ( 3 + 5 x - 8 x ) x - \frac{d x}{d x} ( 3 + 5 x - 8 x )}{x ^{2}}

\frac{d}{d x} (3 + 5 x - 8 x) = - \frac{4}{x} + 5

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

= \frac{( - \frac{4}{x} + 5 ) x - 1 \cdot ( 3 + 5 x - 8 x )}{x ^{2}}

Simplify

\frac{( - \frac{4}{x} + 5 ) x - 1 \cdot ( 3 + 5 x - 8 x )}{x ^{2}} : \frac{4 x - 3}{x ^{2}}

= \frac{4 x - 3}{x ^{2}}

f (x) = cos (a^{3} + x^{3})

y^{^{''}} + 0.5 y^{^{'}} + 4 y = 0

\int 6 x x + 2 d x

\int 8 \frac{x}{4} + 1 d x

\frac{d}{d x} (8 x^{2} + x)

What is the derivative of (3+5x-8sqrt(x)/x) ?
The derivative of (3+5x-8sqrt(x)/x) is (4sqrt(x)-3)/(x^2)
What is the first derivative of (3+5x-8sqrt(x)/x) ?
The first derivative of (3+5x-8sqrt(x)/x) is (4sqrt(x)-3)/(x^2)