"If y = $$\sum\limits_{k = 1}^6 {k{{\cos }^{ - 1}}\left\{ {{3 \over 5}\cos kx - {4 \over 5}\sin kx} \right\}} $$, then ${{dy} \over {dx}}$ at x = 0 is _______."

Question

Accepted Answer

"Put, $\cos \alpha = {3 \over 5},\sin \alpha = {4 \over 5}$

$\therefore {3 \over 5}\cos kx - {4 \over 5}\sin \,kx$

$= \cos \alpha .\cos kx - \sin \alpha .\sin kx$

$= \cos \left( {\alpha + kx} \right)$

So, $$y = \sum\limits_{k = 1}^6 {k{{\cos }^{ - 1}}\left( {\cos \left( {\alpha + kx} \right)} \right)} $$

$= \sum\limits_{k = 1}^6 {\left( {{k^2}x + kx} \right)}$

$\Rightarrow {{dy} \over {dx}} = \sum\limits_{k = 1}^6 {{k^2}}$

$= {{6 \times 7 \times 13} \over 6} = 91$"

If y = $$\sum\limits_{k = 1}^6 {k{{\cos }^{ - 1}}\left\{ {{3 \over 5}\cos kx - {4 \over 5}\sin kx} \right\}} $$,

then ${{dy} \over {dx}}$ at x = 0 is _______.

Solution

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If y = $$\sum\limits_{k = 1}^6 {k{{\cos }^{ - 1}}\left\{ {{3 \over 5}\cos kx - {4 \over 5}\sin kx} \right\}} $$, then ${{dy} \over {dx}}$ at x = 0 is _______.

Solution

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More Differentiation questions

Drill 25 more like these. Every day. Free.

If y = $$\sum\limits_{k = 1}^6 {k{{\cos }^{ - 1}}\left\{ {{3 \over 5}\cos kx - {4 \over 5}\sin kx} \right\}} $$,

then ${{dy} \over {dx}}$ at x = 0 is _______.