# How do you find the derivative of # 6x^(- 7/8)#?

Simplifying provides the solution.

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To find the derivative of (6x^{-7/8}), you can use the power rule for differentiation. The power rule states that if (f(x) = ax^n), then (f'(x) = anx^{n-1}). Applying this rule to (6x^{-7/8}), the derivative is:

[ f'(x) = \frac{-7}{8} \cdot 6x^{-7/8 - 1} ]

Simplify the expression:

[ f'(x) = \frac{-7}{8} \cdot 6x^{-7/8 - 1} = -\frac{7}{4}x^{-15/8} ]

So, the derivative of (6x^{-7/8}) is (-\frac{7}{4}x^{-15/8}).

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