Question

please differentiate log7(log x)

Answer 1

Answer:

Step-by-step explanation:

Let y=log7(logx)

=> y= log(logx)/log 7 (Base changing formula of logarithm)

=> dy/dx= (1/log 7)(1/log x) d/dx (log x)

=> dy/dx = 1/{(log 7)(log x)(x)}

Answer 2

Concept:

The sensitivity of a function's value to a change in its input is measured by the derivative of a function of a real variable.

Given:

log7(log x)

To find:

The derivative of the function

Solution:

A function is given to us in this question

$log_{7} (logx)$

But, we do not solve the base if it's a digit.

Here the base is 7 so first we will change the base before differentiating it.

So now, changing the base,

let y be the function, so

$y=log_{7}(logx) \\y=\frac{log(logx)}{log7}$

So, now since we have changed the base of the function, we can differentiate it

$\frac{dy}{dx} =\frac{dy\frac{log(logx)}{log7} }{dx}\\ \frac{dy}{dx}= \frac{1}{log7}\frac{d(log(logx)}{dx} \\\frac{dy}{dx}=\frac{1}{log7}*\frac{1}{logx}*\frac{d(logx)}{dx} \\\frac{dy}{dx}=\frac{1}{log7}*\frac{1}{logx} *\frac{1}{x} \\\frac{dy}{dx} =\frac{1}{xlog7logx}$

So, the derivative of the function is $\frac{1}{xlog7logx}$

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