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

The derivative of Insqrt(x(1-x)) is (nI(1-2x))/(2sqrt(x(1-x)))

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

The first derivative of Insqrt(x(1-x)) is (nI(1-2x))/(2sqrt(x(1-x)))

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

\frac{n I ( 1 - 2 x )}{2 x ( 1 - x )}

Solution steps

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

Treat

n, I

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= I n \frac{1}{2 x ( 1 - x )} (1 - 2 x)

Simplify

I n \frac{1}{2 x ( 1 - x )} (1 - 2 x) : \frac{n I ( 1 - 2 x )}{2 x ( 1 - x )}

= \frac{n I ( 1 - 2 x )}{2 x ( 1 - x )}

f (x) = \frac{2 x ^{3}}{3} - \frac{x ^{2}}{2} - x

y = x^{3} - 6 x^{2} + 9 x - 8

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

f (x) = 12 + 2 x - x^{2}

f (x) = \frac{x ^{2} - 24}{x - 5}

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