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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\frac{d}{d x} (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}}

\frac{\partial}{\partial x} (tan (x))

6 x^{2}, 0, 1, 5

\int_{- 1}^{3} (2 x)^{3} d x

(7) (0 - 6)

x^{4} + y^{3} x^{5} + 2 y^{^{'}} = 0

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))