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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

25.   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 )

Answers (1)

best_answer

Given,

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

And the Multiplication property of derivative,

\frac{d(y_1y_2)}{dx}=y_1\frac{dy_2}{dx}+y_2\frac{dy_1}{dx}

Also the property 

\frac{d(y_1+y_2)}{dx}=\frac{dy_1}{dx}+\frac{dy_2}{dx}

Applying those properties we get,

\frac{d(( x+ \cos x ) ( x - \tan x ))}{dx}=(x+\cos x)\frac{d(x-\tan x)}{dx}+(x-\tan x)\frac{d(x+\cos x)}{dx}

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

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

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

Posted by

Pankaj Sanodiya

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