What is the derivative of (3x^2+2sqrt(x)/x) ?

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

What is the first derivative of (3x^2+2sqrt(x)/x) ?

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (3 x^{2} + 2 x) = 6 x + \frac{1}{x}

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

= \frac{( 6 x + \frac{1}{x} ) x - 1 \cdot ( 3 x ^{2} + 2 x )}{x ^{2}}

Simplify

\frac{( 6 x + \frac{1}{x} ) x - 1 \cdot ( 3 x ^{2} + 2 x )}{x ^{2}} : \frac{3 x ^{2} - x}{x ^{2}}

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

\frac{d}{d x} (cot (x) csc (x))

g (x) = e^{x^{2} - x}

\frac{d}{d x} (- 2 x + 6)

\int \frac{8}{x ln ( 5 x )} d x

n = 1 \sum \infty \frac{1}{3 n - 1}

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