What is the derivative of xsqrt(1-x) ?

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

What is the first derivative of xsqrt(1-x) ?

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

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

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

Solution steps

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

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

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

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

Simplify

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

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

\frac{d}{d x} (\frac{x - 1}{4})

\frac{d}{d x} (8 arcsin (x^{3}))

\int 7 + x^{2} d x

x^{^{''}} - 0.1 x^{^{'}} + x = 0

y \frac{d y}{d x} = x + 2

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