What is the derivative of $sin (\frac{x}{2}) + cos x$ $sin(x/2)+cosx$ ?

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What is the derivative of $sin (\frac{x}{2}) + cos x$ $sin(x/2)+cosx$ ?

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Answer 1 · 2018-02-03T14:38:29

$\frac{1}{2} cos (\frac{x}{2}) - sin x$ $1/2cos(x/2)-sinx$

Explanation:

$differentiate sin (\frac{x}{2}) using the chain rule$ $"differentiate "sin(x/2)" using the "color(blue)"chain rule"$

$given y = f (g (x)) then$ $"given "y=f(g(x))" then"$

$dy/dx-f'(g(x))xxg'(x)larrcolor(blue)"chain rule"$

$rArrd/dx(sin(x/2)+cosx)$

$=cos(x/2)xxd/dx(1/2x)-sinx$

$=1/2cos(x/2)-sinx$

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What is the derivative of $sin (\frac{x}{2}) + cos x$ $sin(x/2)+cosx$ ?

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