What is the derivative of cos(arcsin(2x)) ?

The derivative of cos(arcsin(2x)) is -(4x)/(sqrt(1-4x^2))

What is the first derivative of cos(arcsin(2x)) ?

The first derivative of cos(arcsin(2x)) is -(4x)/(sqrt(1-4x^2))

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\frac{d}{d x} (cos (arcsin (2 x)))

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

Solution steps

\frac{d}{d x} (cos (arcsin (2 x)))

Simplify

cos (arcsin (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}}

x^{2} - x - 4, - x^{2} + 3 x + 2

\int 12 (y^{4} + 4 y^{2} + 5)^{2} (y^{3} + 2 y) d y

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

\int e^{\frac{x ^{2}}{2}} d x

\frac{d}{d s} (\frac{t}{s})

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