derivative of y=arcsin(x+1) — step-by-step solution

We save the definition:

y = \arcsin (x + 1)

Let's differentiate:

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

Apply the differentiation rule:

\frac{d}{d x} (asin (f)) = \frac{d}{d x} (f) \cdot \frac{1}{\sqrt{1 - f^{2}}}

with f =

x + 1

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

\frac{1 + 0}{\sqrt{1 - {(x + 1)}^{2}}}

▶Derivative:

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