What is the (arcsin(2x))^' ?

The (arcsin(2x))^' is 2/(sqrt(1-4x^2))

What is the first (arcsin(2x))^' ?

The first (arcsin(2x))^' is 2/(sqrt(1-4x^2))

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(arcsin (2 x))^{^{'}}

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

Solution steps

(arcsin (2 x))^{'}

Apply the chain rule:

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

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

(2 x)^{'} = 2

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

Simplify

\frac{1}{1 - ( 2 x ) ^{2}} \cdot 2 : \frac{2}{1 - 4 x ^{2}}

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