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Helen [10]
3 years ago
5

Differentiating Functions of Other Bases In Exercise, find the derivative of the function.

Mathematics
1 answer:
zimovet [89]3 years ago
6 0

Answer:

y' = -\frac{1}{2.3x}

Step-by-step explanation:

The derivative of a*x^{n} is a*n*x^{n-1}. The derivative of 3x^{-1} is -3x^{-2}, for example.

Derivative of the log function:

y = \log_{a}{f(x)}

Has the following derivative

y' = \frac{f'(x)}{\ln{a}*f(x)}

In this problem, we have that:

y = \log_{10}{\frac{3}{x}}

So

a = 10, f(x) = \frac{3}{x} = 3x^{-1}, f'(x) = -3x^{-2}

The derivative of the function is:

y' = \frac{f'(x)}{\ln{a}*f(x)}

y' = \frac{-3x^{-2}}{2.3*3x^{-1}}

y' = -\frac{1}{2.3x}

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