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:

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-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.

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