The derivative of root 1-x^2 is equal to -x divided by root(1-x^{2}). In this post, we learn to find the derivative of square root of 1- x square.

The derivative formula of $\sqrt{1-x^2}$ is given by

$\dfrac{d}{dx} \big( \sqrt{1-x^2}\big) = -\dfrac{x}{\sqrt{1-x^2}}$.

## Derivative of Square Root of 1-x^{2}

**Answer:** The derivative of square root of 1-x^{2} is -x/√(1-x^{2}).

**Explanation:**

To find the derivative of root 1-x^{2}, we will use the following formula:

By chain rule, the derivative of f(x) is equal to $\dfrac{d}{dx}(\sqrt{f(x)})$ $=\dfrac{1}{2\sqrt{f(x)}} \cdot \dfrac{d}{dx}(f(x))$. |

Put f(x) = $\sqrt{1-x^2}$.

So by the above formula, the derivative of root(1-x^{2}) is equal to

$\dfrac{d}{dx}(\sqrt{1-x^2})$ $=\dfrac{1}{2\sqrt{1-x^2}} \cdot \dfrac{d}{dx}(1-x^2)$

= $\dfrac{1}{2\sqrt{1-x^2}} \cdot (-2x)$

= $\dfrac{-2x}{2\sqrt{1-x^2}}$

= $\dfrac{-x}{\sqrt{1-x^2}}$

So the derivative of square root of 1-x^{2} is equal to $\dfrac{-x}{\sqrt{1-x^2}}$, and this is obtained by the chain rule of derivatives.

Related Derivatives:

Derivative of $\dfrac{1}{\sqrt{1-x^2}}$

## FAQs

**Q1: What is the derivative of square root of 1-x**^{2}?

^{2}?

**Answer:** The derivative of square root of 1-x^{2} is equal to -x/√(1-x^{2}).

**Q2: If y=root(1-x**^{2}), then find dy/dx.

^{2}), then find dy/dx.

**Answer:** If y=root(1-x^{2}), then dy/dx= -x/√(1-x^{2}).