What is the derivative of sin(arccos(2x)) ?

The derivative of sin(arccos(2x)) is -(4x)/(sqrt(1-4x^2))

What is the first derivative of sin(arccos(2x)) ?

The first derivative of sin(arccos(2x)) is -(4x)/(sqrt(1-4x^2))

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

- \frac{4 x}{1 - 4 x ^{2}}

Solution steps

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

Simplify

sin (arccos (2 x)) : 1 - 4 x^{2}

= \frac{d}{d x} (1 - 4 x^{2})

Apply the chain rule:

\frac{1}{2 1 - 4 x ^{2}} \frac{d}{d x} (1 - 4 x^{2})

= \frac{1}{2 1 - 4 x ^{2}} \frac{d}{d x} (1 - 4 x^{2})

\frac{d}{d x} (1 - 4 x^{2}) = - 8 x

= \frac{1}{2 1 - 4 x ^{2}} (- 8 x)

Simplify

\frac{1}{2 1 - 4 x ^{2}} (- 8 x) : - \frac{4 x}{1 - 4 x ^{2}}

= - \frac{4 x}{1 - 4 x ^{2}}

What is the derivative of sin(arccos(2x)) ?
The derivative of sin(arccos(2x)) is -(4x)/(sqrt(1-4x^2))
What is the first derivative of sin(arccos(2x)) ?
The first derivative of sin(arccos(2x)) is -(4x)/(sqrt(1-4x^2))