Derivative of x^3 - 2*x at x = c

The calculator will find the derivative of

x^{3} - 2 x

at

x = c

, with steps shown.

Your Input

Find $\frac{d}{dx} \left(x^{3} - 2 x\right)$ and evaluate it at $x = c$ .

Solution

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

{\color{red}\left(\frac{d}{dx} \left(x^{3} - 2 x\right)\right)} = {\color{red}\left(\frac{d}{dx} \left(x^{3}\right) - \frac{d}{dx} \left(2 x\right)\right)}

Apply the constant multiple rule $\frac{d}{dx} \left(c f{\left(x \right)}\right) = c \frac{d}{dx} \left(f{\left(x \right)}\right)$ with $c = 2$ and $f{\left(x \right)} = x$ :

- {\color{red}\left(\frac{d}{dx} \left(2 x\right)\right)} + \frac{d}{dx} \left(x^{3}\right) = - {\color{red}\left(2 \frac{d}{dx} \left(x\right)\right)} + \frac{d}{dx} \left(x^{3}\right)

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

- 2 {\color{red}\left(\frac{d}{dx} \left(x\right)\right)} + \frac{d}{dx} \left(x^{3}\right) = - 2 {\color{red}\left(1\right)} + \frac{d}{dx} \left(x^{3}\right)

Apply the power rule $\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$ with $n = 3$ :

{\color{red}\left(\frac{d}{dx} \left(x^{3}\right)\right)} - 2 = {\color{red}\left(3 x^{2}\right)} - 2

Thus, $\frac{d}{dx} \left(x^{3} - 2 x\right) = 3 x^{2} - 2$ .

Finally, evaluate the derivative at $x = c$ .

$\left(\frac{d}{dx} \left(x^{3} - 2 x\right)\right)|_{\left(x = c\right)} = 3 c^{2} - 2$

Answer

$\frac{d}{dx} \left(x^{3} - 2 x\right) = 3 x^{2} - 2$ A

$\left(\frac{d}{dx} \left(x^{3} - 2 x\right)\right)|_{\left(x = c\right)} = 3 c^{2} - 2$ A

Derivative of x3−2xx^{3} - 2 xx3−2x at x=cx = cx=c

Your Input

Solution

Answer

Derivative of $x^{3} - 2 x$ at $x = c$