|
|
|
|
|
|
|
|
|
|
|
|
Derivative of $$$6 - x^{3}$$$
Related calculators: Logarithmic Differentiation Calculator, Implicit Differentiation Calculator with Steps
Your Input
Find $$$\frac{d}{dx} \left(6 - x^{3}\right)$$$.
Solution
The derivative of a sum/difference is the sum/difference of derivatives:
$${\color{red}\left(\frac{d}{dx} \left(6 - x^{3}\right)\right)} = {\color{red}\left(\frac{d}{dx} \left(6\right) - \frac{d}{dx} \left(x^{3}\right)\right)}$$Apply the power rule $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$ with $$$n = 3$$$:
$$- {\color{red}\left(\frac{d}{dx} \left(x^{3}\right)\right)} + \frac{d}{dx} \left(6\right) = - {\color{red}\left(3 x^{2}\right)} + \frac{d}{dx} \left(6\right)$$The derivative of a constant is $$$0$$$:
$$- 3 x^{2} + {\color{red}\left(\frac{d}{dx} \left(6\right)\right)} = - 3 x^{2} + {\color{red}\left(0\right)}$$Thus, $$$\frac{d}{dx} \left(6 - x^{3}\right) = - 3 x^{2}$$$.
Answer
$$$\frac{d}{dx} \left(6 - x^{3}\right) = - 3 x^{2}$$$A
Please try a new game Rotatly