What is the (cos(arcsin(x)))^' ?

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

What is the first (cos(arcsin(x)))^' ?

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

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(cos (arcsin (x)))^{^{'}}

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

Solution steps

(cos (arcsin (x)))^{'}

Simplify

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

= (1 - x^{2})^{^{'}}

Apply the chain rule:

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

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

(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}}

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