How do you differentiate $y = 1/2 x + 1/4sin2x$ ?

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Answer 1 · 2016-12-20T15:36:13

$dy/dx = cos^2x$

This can be rewritten as follows using the identity $sin2theta = 2sinthetacostheta$ and a little algebra.

$y = 1/2x + 1/4(2sinxcosx)$

$y = 1/2x + 1/2sinxcosx$

$y = 1/2(x + sinxcosx)$

$2y = x + sinxcosx$

$2(dy/dx) = 1 + cosx(cosx) + sinx(-sinx)$

$2(dy/dx) = 1 + cos^2x - sin^2x$

Use the identity $cos^2theta + sin^2theta = 1 ->1 - sin^2theta = cos^2theta$ :

$2(dy/dx) = cos^2x + cos^2x$

$2(dy/dx) = 2cos^2x$

$dy/dx = (2cos^2x)/2$

$dy/dx= cos^2x$

Hopefully this helps!

How do you differentiate y = 1/2 x + 1/4sin2xy = 1/2 x + 1/4sin2x?