Question

log(tan5x) differentiate with respect to x

Answer 1

the differentiation of log(tan5x) is:-
5/tan5x (sec5x)square.

Answer 2

Given:

y = log(tan5x) [say]

To Find:

The value obtained on differentiating y with respect to x.

Solution:

Since, in this question, there are functions within functions, we will have to use the chain rule of differentiation, according to which we have to differentiate the functions as a chain, i.e., differentiate functions within a function separately and then multiply it with the result.

Since, y = log(tan5x)

Let's differentiate it with respect to x,

$\Rightarrow \dfrac{dy}{dx} = \dfrac{d}{dx}[log(tan5x)]\\\\\Rightarrow \dfrac{dy}{dx} = \dfrac{1}{tan5x}\dfrac{d}{dx}(tan5x)\\\\\Rightarrow \dfrac{dy}{dx} = \dfrac{1}{tan5x} \cdot sec^25x \cdot \dfrac{d}{dx} (5x)\\\\\Rightarrow \dfrac{dy}{dx} = \dfrac{1}{tan5x} \cdot sec^25x \cdot 5\\\\\Rightarrow \dfrac{dy}{dx} = \dfrac{5 sec^25x}{tan 5x}$

Thus, the differentiation of log(tan5x) with respect to x = $\dfrac{5 sec^25x}{tan(5x)}$