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Derivative of $$$x^{6} - 7$$$
Related calculators: Logarithmic Differentiation Calculator, Implicit Differentiation Calculator with Steps
Your Input
Find $$$\frac{d}{dx} \left(x^{6} - 7\right)$$$.
Solution
The derivative of a sum/difference is the sum/difference of derivatives:
$${\color{red}\left(\frac{d}{dx} \left(x^{6} - 7\right)\right)} = {\color{red}\left(\frac{d}{dx} \left(x^{6}\right) - \frac{d}{dx} \left(7\right)\right)}$$The derivative of a constant is $$$0$$$:
$$- {\color{red}\left(\frac{d}{dx} \left(7\right)\right)} + \frac{d}{dx} \left(x^{6}\right) = - {\color{red}\left(0\right)} + \frac{d}{dx} \left(x^{6}\right)$$Apply the power rule $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$ with $$$n = 6$$$:
$${\color{red}\left(\frac{d}{dx} \left(x^{6}\right)\right)} = {\color{red}\left(6 x^{5}\right)}$$Thus, $$$\frac{d}{dx} \left(x^{6} - 7\right) = 6 x^{5}$$$.
Answer
$$$\frac{d}{dx} \left(x^{6} - 7\right) = 6 x^{5}$$$A
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