How do you find the derivative of arcsin(2x)?

2 Answers
Mar 1, 2016

d/dx (arcsin(2x))=2/(sqrt(1-(2x)^2) )

Explanation:

Use chain rule to find the derivative. The derivative of arcsin x is 1/square root of 1-x^2 and then multiply by the derivative of 2x.

Mar 1, 2016

\frac{d}{dx}(\arcsin (2x))=\frac{2}{\sqrt{1-4x^2}}

Explanation:

\frac{d}{dx}(\arcsin (2x))

Applying chain rule as: \frac{df(u)}{dx}=\frac{df}{du}\cdot \frac{du}{dx}

Let 2x=u

=\frac{d}{du}(\arcsin (u)). frac{d}{dx}(2x)

\frac{d}{du}(\arcsin(u)) = \frac{1}{\sqrt{1-u^2}}
{Applying the common derivative : \frac{d}{du}(\arcsin (u))=\frac{1}{\sqrt{1-u^2}} }

And,
\frac{d}{dx}(2x)=2

Substituting back u=2x,

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

Simplifying,
=\frac{2}{\sqrt{1-4x^2}}