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Popular >

derivative of (2x-x^2/(sqrt(x)))

Solution

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

Solution

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

Solution steps

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

Simplify

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

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

Apply the Product Rule:

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

f = x, g = 2 - x

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

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

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

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

Simplify

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

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

Popular Examples

2y^{''}+8y^'+80y=40cos(8t)

2 y^{^{''}} + 8 y^{^{'}} + 80 y = 40 cos (8 t)

y^{''}+5y^'+3y=0

y^{^{''}} + 5 y^{^{'}} + 3 y = 0

(6x+1)y^2(dy)/(dx)+3x^2+2y^3=0

(6 x + 1) y^{2} \frac{d y}{d x} + 3 x^{2} + 2 y^{3} = 0

limit as x approaches-1+of sqrt(3x+3)-5

x \to - 1 + lim (3 x + 3 - 5)

derivative of y=cos(3x^2)derivative of

y = cos (3 x^{2})

Frequently Asked Questions (FAQ)

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