How do you differentiate arcsin(2x)?

2 Answers
Jim G.
Jul 30, 2017

2/(sqrt(1-4x^2)

Explanation:

•color(white)(x)d/dx(sin^-1x)=1/(sqrt(1-x^2))

"differentiate using the "color(blue)"chain rule"

•color(white)(x)d/dx(sin^-1(f(x)))=1/(sqrt(1-(f(x))^2)xxf'(x)

rArrd/dx(sin^-1(2x))

=1/(sqrt(1-(2x)^2))xxd/dx(2x)

=2/(sqrt(1-4x^2))

Narad T.
Jul 30, 2017

The derivative is =2/sqrt(1-4x^2)

Explanation:

Let y=arcsin(2x)

siny=2x

Differentiating with respect to x

dy/dxcosy=2

dy/dx=2/cosy

We know that

sin^2y+cos^2y=1

cos^2y=1-sin^2y=1-4x^2

cosy=sqrt(1-4x^2)

Therefore,

dy/dx=2/sqrt(1-4x^2)

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