Find the derivative of the following functions (it is to be understood that $a, b, c, d, p, q, r$ and $s$ are fixed non-zero constants and $m$ and $n$ are integers) : $\frac{x}{1 + tan x}$

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Solution

Let $f (x) = \frac{x}{1 + tan x}$
$f^{'} (x) = \frac{(1 + tan x) \frac{d}{d x} (x) - x \frac{d}{d x} (1 + tan x)}{{(1 + tan x)}^{2}}$
$= \frac{1 + tan x - x {sec}^{2} x}{{(1 + tan x)}^{2}}$

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Find the derivative of the following functions (it is to be understood that a,b,c,d,p,q,r and s are fixed non-zero constants and m and n are integers) : x1+tanx

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Find the derivative of the following functions (it is to be understood that $a, b, c, d, p, q, r$ and $s$ are fixed non-zero constants and $m$ and $n$ are integers) : $\frac{x}{1 + tan x}$

Let $f (x) = \frac{x}{1 + tan x}$
$f^{'} (x) = \frac{(1 + tan x) \frac{d}{d x} (x) - x \frac{d}{d x} (1 + tan x)}{{(1 + tan x)}^{2}}$
$= \frac{1 + tan x - x {sec}^{2} x}{{(1 + tan x)}^{2}}$