What is the derivative of (3x^2-4x)/(sqrt(x)) ?

The derivative of (3x^2-4x)/(sqrt(x)) is (9x-4)/(2sqrt(x))

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

The first derivative of (3x^2-4x)/(sqrt(x)) is (9x-4)/(2sqrt(x))

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derivative of

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

\frac{9 x - 4}{2 x}

Solution steps

\frac{d}{d x} (\frac{3 x ^{2} - 4 x}{x})

Simplify

\frac{3 x ^{2} - 4 x}{x} : x (3 x - 4)

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = 3 x - 4

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

\frac{d}{d x} (x) = \frac{1}{2 x}

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

= \frac{1}{2 x} (3 x - 4) + 3 x

Simplify

\frac{1}{2 x} (3 x - 4) + 3 x : \frac{9 x - 4}{2 x}

= \frac{9 x - 4}{2 x}

\int x + x d x

f (x) = 3 x + \frac{2}{x}, at x = 2

\frac{d y}{d x} + 7 x^{6} y = x^{6}

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

\frac{d}{d x} (e^{k^{2} x})

What is the derivative of (3x^2-4x)/(sqrt(x)) ?
The derivative of (3x^2-4x)/(sqrt(x)) is (9x-4)/(2sqrt(x))
What is the first derivative of (3x^2-4x)/(sqrt(x)) ?
The first derivative of (3x^2-4x)/(sqrt(x)) is (9x-4)/(2sqrt(x))