What is the derivative of 2aarccos(sqrt(2x)) ?

The derivative of 2aarccos(sqrt(2x)) is -(sqrt(2)a)/(sqrt(x)\sqrt{1-2x)}

What is the first derivative of 2aarccos(sqrt(2x)) ?

The first derivative of 2aarccos(sqrt(2x)) is -(sqrt(2)a)/(sqrt(x)\sqrt{1-2x)}

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\frac{d}{d x} (2 a arccos (2 x))

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

Solution steps

\frac{d}{d x} (2 a arccos (2 x))

Simplify

2 a arccos (2 x) : 2 a arccos (2 x)

= \frac{d}{d x} (2 a arccos (2 x))

Take the constant out:

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

= 2 a \frac{d}{d x} (arccos (2 x))

Apply the chain rule:

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

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

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

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

Simplify

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

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

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What is the derivative of 2aarccos(sqrt(2x)) ?
The derivative of 2aarccos(sqrt(2x)) is -(sqrt(2)a)/(sqrt(x)\sqrt{1-2x)}
What is the first derivative of 2aarccos(sqrt(2x)) ?
The first derivative of 2aarccos(sqrt(2x)) is -(sqrt(2)a)/(sqrt(x)\sqrt{1-2x)}