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

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

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

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

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

\frac{5 x ^{2} - 4}{2 x}

Solution steps

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

Simplify

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

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

Apply the Product Rule:

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

f = x, g = x^{2} - 4

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

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

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

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

Simplify

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

= \frac{5 x ^{2} - 4}{2 x}

\frac{\partial}{\partial z} (\frac{x}{y} - yz)

\frac{\partial}{\partial x} (x + y sin (t))

f (x) = - 7 x

x \to 0 - lim (\frac{∣ 3 x ∣}{x})

\frac{d}{d x} (x - 2 cos (x))

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