derivative of sqrt(1-x^2) — step-by-step solution

Let's perform the differentiation:

{(\sqrt{1 - x^{2}})}^{'}

Apply the differentiation rule:

{(\sqrt{f})}^{'} = {(f)}^{'} \cdot \frac{1}{2 \sqrt{f}}

with f =

1 - x^{2}

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

ℹ

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

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

‖

{(1 - x^{2})}^{'}

0 + {(- x^{2})}^{'}

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

- \frac{2 x}{2 \cdot \sqrt{1 - x^{2}}}

▶Derivative:

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