If y = ∑ _ k = 1 ^ 6 k ^ - 1 \ (3)/(5)coskx - (4)/(5)sinkx\ then...

For, small values near $0$, i.e., \left|x\right| < < . . 1$</p><p>$y = \mathop{∑}_{k = 1}^{6}k\cos^{- 1}\left(coskx \cdot cos\alpha - sinkx \cdot sin\alpha\right)

= \mathop{∑}_{k = 1}^{6}k\cos^{- 1}\left(\cos \left(kx + \alpha\right)\right)$<br />$= \mathop{∑}_{k = 1}^{6}k \left(kx + \alpha\right)$</p><p>$= \mathop{∑}_{k = 1}^{6}\left({k}^{2}x + k\alpha\right)

\dfrac{dy}{dx} =\mathop{∑}_{k = 1}^{6}{k}^{2} = \dfrac{6\left(7\right)\left(13\right)}{6} = 91