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Find the derivative of the following functions (it is to be un

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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) : $(x + cos x) (x - tan x)$

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Lucas Discussed

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) :

(x + cos x) (x - tan x)

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Text solutionVerified

Let

f (x) = (x + cos x) (x - tan x)

Thus by product rule,

f^{'} (x) = (x + cos x) \frac{d}{d x} (x - tan x) + (x - tan x) \frac{d}{d x} (x + cos x)

= (x + cos x) (1 - sec^{2} x) + (x - tan x) (1 - sin x)

= (x + cos x) (- tan^{2} x) + (x - tan x) (1 - sin x)

= - tan^{2} x (x + cos x) + (x - tan x) (1 - sin x)

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Question Text	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) : $(x + cos x) (x - tan x)$
Answer Type	Text solution:1
Upvotes	150