What is the derivative of y=axsqrt(1-x) ?

The derivative of y=axsqrt(1-x) is (a(-3x+2))/(2sqrt(1-x))

What is the first derivative of y=axsqrt(1-x) ?

The first derivative of y=axsqrt(1-x) is (a(-3x+2))/(2sqrt(1-x))

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derivative of

y = a x 1 - x

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= a \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

= a (\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}

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

Simplify

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

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

What is the derivative of y=axsqrt(1-x) ?
The derivative of y=axsqrt(1-x) is (a(-3x+2))/(2sqrt(1-x))
What is the first derivative of y=axsqrt(1-x) ?
The first derivative of y=axsqrt(1-x) is (a(-3x+2))/(2sqrt(1-x))