Derivative of $$$2 - x^{4}$$$
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Your Input
Find $$$\frac{d}{dx} \left(2 - x^{4}\right)$$$.
Solution
The derivative of a sum/difference is the sum/difference of derivatives:
$${\color{red}\left(\frac{d}{dx} \left(2 - x^{4}\right)\right)} = {\color{red}\left(\frac{d}{dx} \left(2\right) - \frac{d}{dx} \left(x^{4}\right)\right)}$$The derivative of a constant is $$$0$$$:
$${\color{red}\left(\frac{d}{dx} \left(2\right)\right)} - \frac{d}{dx} \left(x^{4}\right) = {\color{red}\left(0\right)} - \frac{d}{dx} \left(x^{4}\right)$$Apply the power rule $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$ with $$$n = 4$$$:
$$- {\color{red}\left(\frac{d}{dx} \left(x^{4}\right)\right)} = - {\color{red}\left(4 x^{3}\right)}$$Thus, $$$\frac{d}{dx} \left(2 - x^{4}\right) = - 4 x^{3}$$$.
Answer
$$$\frac{d}{dx} \left(2 - x^{4}\right) = - 4 x^{3}$$$A