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Derivative of $$$- x^{8}$$$
Related calculators: Logarithmic Differentiation Calculator, Implicit Differentiation Calculator with Steps
Your Input
Find $$$\frac{d}{dx} \left(- x^{8}\right)$$$.
Solution
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 $$$c = -1$$$ and $$$f{\left(x \right)} = x^{8}$$$:
$${\color{red}\left(\frac{d}{dx} \left(- x^{8}\right)\right)} = {\color{red}\left(- \frac{d}{dx} \left(x^{8}\right)\right)}$$Apply the power rule $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$ with $$$n = 8$$$:
$$- {\color{red}\left(\frac{d}{dx} \left(x^{8}\right)\right)} = - {\color{red}\left(8 x^{7}\right)}$$Thus, $$$\frac{d}{dx} \left(- x^{8}\right) = - 8 x^{7}$$$.
Answer
$$$\frac{d}{dx} \left(- x^{8}\right) = - 8 x^{7}$$$A
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