What is the derivative of (5x^2-sqrt(x)/x) ?

The derivative of (5x^2-sqrt(x)/x) is (sqrt(x)+10x^2)/(2x^2)

What is the first derivative of (5x^2-sqrt(x)/x) ?

The first derivative of (5x^2-sqrt(x)/x) is (sqrt(x)+10x^2)/(2x^2)

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

\frac{x + 10 x ^{2}}{2 x ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 5 x ^{2} - x ) x - \frac{d x}{d x} ( 5 x ^{2} - x )}{x ^{2}}

\frac{d}{d x} (5 x^{2} - x) = 10 x - \frac{1}{2 x}

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

= \frac{( 10 x - \frac{1}{2 x} ) x - 1 \cdot ( 5 x ^{2} - x )}{x ^{2}}

Simplify

\frac{( 10 x - \frac{1}{2 x} ) x - 1 \cdot ( 5 x ^{2} - x )}{x ^{2}} : \frac{x + 10 x ^{2}}{2 x ^{2}}

= \frac{x + 10 x ^{2}}{2 x ^{2}}

\int \frac{7 ( x ^{2} + 4 )}{x ( x ^{2} + 7 )} d x

t \to 0 lim (sin (4 t))

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

\frac{\partial}{\partial z} (x^{2} y^{4} + z^{3})

\int \frac{x}{x ^{2} - 4} d x

What is the derivative of (5x^2-sqrt(x)/x) ?
The derivative of (5x^2-sqrt(x)/x) is (sqrt(x)+10x^2)/(2x^2)
What is the first derivative of (5x^2-sqrt(x)/x) ?
The first derivative of (5x^2-sqrt(x)/x) is (sqrt(x)+10x^2)/(2x^2)