Derivative of $1 - x^{2}$

The calculator will find the derivative of

1 - x^{2}

, with steps shown.

Find $\frac{d}{dx} \left(1 - x^{2}\right)$ .

The derivative of a sum/difference is the sum/difference of derivatives:

{\color{red}\left(\frac{d}{dx} \left(1 - x^{2}\right)\right)} = {\color{red}\left(\frac{d}{dx} \left(1\right) - \frac{d}{dx} \left(x^{2}\right)\right)}

Apply the power rule $\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$ with $n = 2$ :

- {\color{red}\left(\frac{d}{dx} \left(x^{2}\right)\right)} + \frac{d}{dx} \left(1\right) = - {\color{red}\left(2 x\right)} + \frac{d}{dx} \left(1\right)

The derivative of a constant is $0$ :

- 2 x + {\color{red}\left(\frac{d}{dx} \left(1\right)\right)} = - 2 x + {\color{red}\left(0\right)}

Thus, $\frac{d}{dx} \left(1 - x^{2}\right) = - 2 x$ .

$\frac{d}{dx} \left(1 - x^{2}\right) = - 2 x$ A

Derivative of 1−x21 - x^{2}1−x2