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2 years ago

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

Mathematics

1 answer:

densk [106]2 years ago

7 0

Answer:

The derivative of the function is:

$g'(x) = \frac{1}{1.6094x}$

Step-by-step explanation:

If we have a function in the following format:

$g(x) = \log_{a}{f(x)}$

This function has the following derivative

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

In this problem, we have that:

$g(x) = \log_{5}{x}$

So $f(x) = x, f'(x) = 1, a = 5$

The derivative is

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

$g'(x) = \frac{1}{x*\ln{5}}$

$g'(x) = \frac{1}{1.6094x}$

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2 years ago

Find the vertex and length of the latus rectum for the parabola. y=1/6(x-8)^2+6

Ivan

Step-by-step explanation:

If the parabola has the form

$y = a(x - h)^2 + k$ (vertex form)

then its vertex is located at the point (h, k). Therefore, the vertex of the parabola

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To find the length of the parabola's latus rectum, we need to find its focal length <em>f</em>. Luckily, since our equation is in vertex form, we can easily find from the focus (or focal point) coordinate, which is

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where $\frac{1}{4a}$ is called the focal length or distance of the focus from the vertex. So from our equation, we can see that the focal length <em>f</em> is