If y=cosx +sinx,then dydx at x=2π3 is a−1bwhere a and b are prime numbers, then a+b is

at x=2π3 ⇒y=sinx−cosx ⇒dydx=cosx+sinx ⇒dydxx=2π3=3−12⇒a=3; b=2

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If $y = |cosx| + |sinx|, then \frac{dy}{dx} at x = \frac{2 π}{3}$ is $\frac{\sqrt{a} - 1}{b}$ where a and b are prime numbers, then $a + b$ is

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Detailed Solution

at $x = \frac{2 π}{3} \Rightarrow y = sinx - cosx \Rightarrow \frac{dy}{dx} = cosx + sinx \Rightarrow$ ${(\frac{dy}{dx})}_{x = \frac{2 π}{3}} = \frac{\sqrt{3} - 1}{2} \Rightarrow a = 3; b = 2$

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