What is (\partial)/(\partial x)(arcsin(2x)) ?

The answer to (\partial)/(\partial x)(arcsin(2x)) is 2/(sqrt(1-4x^2))

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(\partial)/(\partial x)(arcsin(2x))

\frac{\partial}{\partial x} (arcsin (2 x))

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

Solution steps

\frac{\partial}{\partial x} (arcsin (2 x))

Apply the chain rule:

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

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

\frac{\partial}{\partial 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}}

What is (\partial)/(\partial x)(arcsin(2x)) ?
The answer to (\partial)/(\partial x)(arcsin(2x)) is 2/(sqrt(1-4x^2))