Question

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

y = log2 1/x^2

Answer 1

`\displaystyle(dy)/(dx) = (-2)/(x\log 2)`

Explanation:

We are given the function:

`y = \log_2\bigg((1)/(x^2)\bigg)`

We have to differentiate the given function.

Formula used:

`\log_a b = (\log b)/(\log a)\\\\(d(\log x))/(dx) = (1)/(x)\\\\(d(x^n))/(dx) = nx^(n-1)`

The derivation takes place in the following manner:

`\displaystyle(dy)/(dx) = (d)/(dx) \bigg(\log_2(1)/(x^2)\bigg)\\\\=(d)/(dx)\bigg((\log((1)/(x^2)))/(\log 2)\bigg)\\\\=(1)/(\log 2)(d)/(dx) \bigg(\log(1)/(x^2)\bigg)\\\\=(1)/(\log 2)\bigg((1)/((1)/(x^2))\bigg)(d)/(dx)((1)/(x^2))\\\\=(x^2)/(\log 2)\bigg((-2)/(x^3)\bigg)\\\\=(-2)/(x\log 2)`