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

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

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

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

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derivative of

cos (arcsin (x))

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

Solution steps

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

Simplify

cos (arcsin (x)) : 1 - x^{2}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

y^{^{'}} = (t + y) 2 - 1, y (1) = 6

\frac{2}{x ^{3}}

f (x) = 2 sin^{2} (π x), at x = \frac{3}{4}

\frac{d}{d t} (sin (a t))

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