# Find Derivative of root 1-x^2

The derivative of root 1-x^2 is equal to -x divided by root(1-x2). 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-x2

Answer: The derivative of square root of 1-x2 is -x/√(1-x2).

Explanation:

To find the derivative of root 1-x2, we will use the following formula:

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

So by the above formula, the derivative of root(1-x2) 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-x2 is equal to $\dfrac{-x}{\sqrt{1-x^2}}$, and this is obtained by the chain rule of derivatives.

Related Derivatives:

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

Derivative of $\sqrt{\sin x}$

Derivative of $\sqrt{\cos x}$

Derivative of sinx/x

Derivative of sin3x

Derivative of sin5x

## FAQs

### Q1: What is the derivative of square root of 1-x2?

Answer: The derivative of square root of 1-x2 is equal to -x/√(1-x2).

### Q2: If y=root(1-x2), then find dy/dx.

Answer: If y=root(1-x2), then dy/dx= -x/√(1-x2).