3 Marks Question

Question 13 Marks

Find the derivative of function $cosec\ x \cot x.$

Answer

Here $f (x) = cosec\ x \cot x$
$\therefore f'(x) = \frac{d}{{dx}} [cosec\ x \cot x]$
$= cosec\ x \frac{d}{{dx}}\ (\cot x) + \cot x \frac{d}{{dx}} (cosec\ x)$
$= cosec\ x . – cosec^2 x + \cot x . – cosec\ x \cot x$
$= - cosec^3 x – cosec\ x \cot^2 x.$

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Question 23 Marks

Find the derivative of $\frac{2}{{x + 1}} - \frac{{{x^2}}}{{3x - 1}}$

Answer

Here $f(x) = \frac{2}{{x + 1}} - \frac{{{x^2}}}{{3x - 1}}$
$\therefore \;f{\text{'}}(x) = \frac{d}{{dx}}\left[ {\frac{2}{{x + 1}} - \frac{{{x^2}}}{{3x - 1}}} \right]$$= \frac{d}{{dx}}\left( {\frac{2}{{x + 1}}} \right) - \frac{d}{{dx}}\left( {\frac{{{x^2}}}{{3x - 1}}} \right)$
$= \frac{{(x + 1)\frac{d}{{dx}}(2) - 2\frac{d}{{dx}}(x + 1)}}{{{{(x + 1)}^2}}}$$- \frac{{(3x - 1)\frac{d}{{dx}}({x^2}) - {x^2}\frac{d}{{dx}}(3x - 1)}}{{{{(3x - 1)}^2}}}$
$ = \frac{{(x + 1) \times 0 - 2 \times 1}}{{{{(x + 1)}^2}}} - \frac{{(3x - 1)(2x) - {x^2 } \times 3}}{{{{(3x - 1)}^2}}}$
$= \frac{{ - 2}}{{{{(x + 1)}^2}}} - \frac{{6{x^2} - 2x - 3{x^2}}}{{{{(3x - 1)}^2}}}$$ = \frac{{ - 2}}{{{{(x + 1)}^2}}} - \frac{{3{x^2} - 2x}}{{{{(3x - 1)}^2}}}$

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Question 33 Marks

Find the derivative of function $2 \tan x - 7 \sec x$

Answer

Here $f(x) = 2 \tan x - 7 \sec x$
$\therefore {\text{f}}(x) = \frac{d}{{dx}}[2\tan x - 7\sec x]$
$= 2\frac{d}{{dx}}(\tan x) - 7\frac{d}{{dx}}(\sec x)$
$= 2 \sec^2x - 7 \sec x \tan x$

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Maths 3 Marks Question

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