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Derivative of $$$x^{3} - 5$$$
Related calculators: Logarithmic Differentiation Calculator, Implicit Differentiation Calculator with Steps
Your Input
Find $$$\frac{d}{dx} \left(x^{3} - 5\right)$$$.
Solution
The derivative of a sum/difference is the sum/difference of derivatives:
$${\color{red}\left(\frac{d}{dx} \left(x^{3} - 5\right)\right)} = {\color{red}\left(\frac{d}{dx} \left(x^{3}\right) - \frac{d}{dx} \left(5\right)\right)}$$Apply the power rule $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$ with $$$n = 3$$$:
$${\color{red}\left(\frac{d}{dx} \left(x^{3}\right)\right)} - \frac{d}{dx} \left(5\right) = {\color{red}\left(3 x^{2}\right)} - \frac{d}{dx} \left(5\right)$$The derivative of a constant is $$$0$$$:
$$3 x^{2} - {\color{red}\left(\frac{d}{dx} \left(5\right)\right)} = 3 x^{2} - {\color{red}\left(0\right)}$$Thus, $$$\frac{d}{dx} \left(x^{3} - 5\right) = 3 x^{2}$$$.
Answer
$$$\frac{d}{dx} \left(x^{3} - 5\right) = 3 x^{2}$$$A
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