Derivative of $$$5 - 6 x^{4}$$$
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Your Input
Find $$$\frac{d}{dx} \left(5 - 6 x^{4}\right)$$$.
Solution
The derivative of a sum/difference is the sum/difference of derivatives:
$${\color{red}\left(\frac{d}{dx} \left(5 - 6 x^{4}\right)\right)} = {\color{red}\left(\frac{d}{dx} \left(5\right) - \frac{d}{dx} \left(6 x^{4}\right)\right)}$$The derivative of a constant is $$$0$$$:
$${\color{red}\left(\frac{d}{dx} \left(5\right)\right)} - \frac{d}{dx} \left(6 x^{4}\right) = {\color{red}\left(0\right)} - \frac{d}{dx} \left(6 x^{4}\right)$$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 $$$c = 6$$$ and $$$f{\left(x \right)} = x^{4}$$$:
$$- {\color{red}\left(\frac{d}{dx} \left(6 x^{4}\right)\right)} = - {\color{red}\left(6 \frac{d}{dx} \left(x^{4}\right)\right)}$$Apply the power rule $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$ with $$$n = 4$$$:
$$- 6 {\color{red}\left(\frac{d}{dx} \left(x^{4}\right)\right)} = - 6 {\color{red}\left(4 x^{3}\right)}$$Thus, $$$\frac{d}{dx} \left(5 - 6 x^{4}\right) = - 24 x^{3}$$$.
Answer
$$$\frac{d}{dx} \left(5 - 6 x^{4}\right) = - 24 x^{3}$$$A