What is the derivative of y=arcsin(2x+1) ?

The derivative of y=arcsin(2x+1) is 1/(sqrt(-x(x+1)))

What is the first derivative of y=arcsin(2x+1) ?

The first derivative of y=arcsin(2x+1) is 1/(sqrt(-x(x+1)))

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derivative

\frac{1}{- x ( x + 1 )}

Solution steps

\frac{d}{d x} (arcsin (2 x + 1))

Apply the chain rule:

\frac{1}{1 - ( 2 x + 1 ) ^{2}} \frac{d}{d x} (2 x + 1)

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

\frac{d}{d x} (2 x + 1) = 2

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

Simplify

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

= \frac{1}{- x ( x + 1 )}

What is the derivative of y=arcsin(2x+1) ?
The derivative of y=arcsin(2x+1) is 1/(sqrt(-x(x+1)))
What is the first derivative of y=arcsin(2x+1) ?
The first derivative of y=arcsin(2x+1) is 1/(sqrt(-x(x+1)))