Question

differentiation plz solve

Answer 1

$\sin(x) + \cos( \gamma ) = 1 \\ \\ Differenciating \: \: w.r.t. \: \: x \: , \\ \\ \cos(x) - \sin( \gamma ) \frac{d \gamma }{dx} = 0 \\ \\ \: \: \: \: \: \: \frac{d \gamma }{dx} = \frac{ \cos(x) }{ \sin( \gamma ) } \\ \\ Differenciating \: \: w.r.t. \: \: x \: \: again \: , \\ \\ \frac{d {}^{2} \gamma }{dx {}^{2} } = \frac{ - \sin( \gamma ) \sin(x) - \cos(x ) \cos( \gamma ) }{ \sin {}^{2} ( \gamma ) } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \large \: \boxed {\frac{d {}^{2} \gamma }{dx {}^{2} } = \frac{ - \cos(x - \gamma ) }{ \sin {}^{2} ( \gamma ) } }$