Question

if y= (sin x/2 + cos x/2)^2 then find dy/dx at x=π/6

Answer 1

hope u get the solution

Answer 2

The answer is $\frac{\sqrt{3}}{2}$.

Step-by-step explanation:

Given:

$\rightarrow \: y = {( \sin( \frac{x}{2} ) + \cos( \frac{x}{2} ) )}^{2} \\ \rightarrow \: y = { \sin }^{2} ( \frac{x}{2} ) + { \cos }^{2} ( \frac{x}{2} ) + 2 \sin( \frac{x}{2} ) \cos( \frac{x}{2} ) \\ \rightarrow \: y = 1 + \sin(x)$

On differentiating on both side with respect to x,

$\rightarrow \: \frac{\mathrm{d} y}{\mathrm{d} x} = \frac{\mathrm{d} }{\mathrm{d} x}(1 + \sin(x) ) \\ \rightarrow \: \frac{\mathrm{d} y}{\mathrm{d} x} = \frac{\mathrm{d} }{\mathrm{d} x} \sin(x) \\ \rightarrow \: \frac{\mathrm{d} y}{\mathrm{d} x} = \cos(x) \\ \: \frac{\mathrm{d} y}{\mathrm{d} x} \: at \: x \rightarrow \frac{\pi}{6} = \cos( \frac{\pi}{6} ) = \frac{ \sqrt{3} }{2}$

The answer is $\frac{\sqrt{3}}{2}$