Question

If y=sinx/1+cosx then dy/dx

Answer 1

$\huge \bold{ \red {\underline {\underline {ANSWER!}}}}$

${\star} \: \: {\blue{\underline {\underline{solution}}}} \blue :$

$y = \frac{sinx}{1 + cosx} \\ \longrightarrow \frac{d}{dx}y = \frac{d}{dx}(\frac{sinx}{1 + cosx}) \\ \longrightarrow\frac{d}{dx}y = \frac{d}{dx}tan( \frac{x}{2} ) \\ \longrightarrow \: \frac{d}{dx}y = \frac{d}{dx}tan \frac{x}{2} \times \frac{d}{dx} (\frac{x}{2} ) \\ \longrightarrow \: \frac{d}{dx}y = { \sec( \frac{x}{2} ) }^{2} \times \frac{1}{2} \\ \longrightarrow \: {\boxed{\frac{d}{dx}y = \frac{ { \sec(x) }^{2} }{2} }}$

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