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

The derivative of (x-x^2/(sqrt(x))) is (1-3x)/(2sqrt(x))

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

The first derivative of (x-x^2/(sqrt(x))) is (1-3x)/(2sqrt(x))

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

\frac{1 - 3 x}{2 x}

Solution steps

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

Simplify

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

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

Apply the Product Rule:

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

f = x, g = 1 - x

= \frac{d}{d x} (x) (1 - x) + \frac{d}{d x} (1 - x) x

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

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

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

Simplify

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

= \frac{1 - 3 x}{2 x}

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

- 4 (x - 9)^{3}

(sin (x)), \frac{π}{2}

n = 1 \sum \infty \frac{2 n}{3 n}

1 + x^{2}

What is the derivative of (x-x^2/(sqrt(x))) ?
The derivative of (x-x^2/(sqrt(x))) is (1-3x)/(2sqrt(x))
What is the first derivative of (x-x^2/(sqrt(x))) ?
The first derivative of (x-x^2/(sqrt(x))) is (1-3x)/(2sqrt(x))