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Derivative of $$$x^{8} - 33$$$
Related calculators: Logarithmic Differentiation Calculator, Implicit Differentiation Calculator with Steps
Your Input
Find $$$\frac{d}{dx} \left(x^{8} - 33\right)$$$.
Solution
The derivative of a sum/difference is the sum/difference of derivatives:
$${\color{red}\left(\frac{d}{dx} \left(x^{8} - 33\right)\right)} = {\color{red}\left(\frac{d}{dx} \left(x^{8}\right) - \frac{d}{dx} \left(33\right)\right)}$$Apply the power rule $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$ with $$$n = 8$$$:
$${\color{red}\left(\frac{d}{dx} \left(x^{8}\right)\right)} - \frac{d}{dx} \left(33\right) = {\color{red}\left(8 x^{7}\right)} - \frac{d}{dx} \left(33\right)$$The derivative of a constant is $$$0$$$:
$$8 x^{7} - {\color{red}\left(\frac{d}{dx} \left(33\right)\right)} = 8 x^{7} - {\color{red}\left(0\right)}$$Thus, $$$\frac{d}{dx} \left(x^{8} - 33\right) = 8 x^{7}$$$.
Answer
$$$\frac{d}{dx} \left(x^{8} - 33\right) = 8 x^{7}$$$A
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