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Popular >

derivative of sin(arccos(2x))

Solution

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

Solution

- \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}}

Popular Examples

derivative of 5cos(4ln(x))

\frac{d}{d x} (5 cos (4 ln (x)))

derivative of sqrt(8x)-sqrt(3x)

\frac{d}{d x} (8 x - 3 x)

integral from 0 to 30 of 9sqrt(x)

\int_{0}^{30} 9 x d x

(\partial)/(\partial u)(v/u)

\frac{\partial}{\partial u} (\frac{v}{u})

integral from 0 to 3 of |2x-4|

\int_{0}^{3} ∣ 2 x - 4 ∣ d x

Frequently Asked Questions (FAQ)

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))