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Differentiate following w.r.t. \( x \cos ( \sqrt 3 x )\)

1 Answer

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  • $\large\frac{dx}{dx}$$(uv)=uv'+vu'$
Step 1:
Given :
$y=x\cos(\sqrt 3x)$
$\large\frac{dx}{dx}$$(uv)=uv'+vu'$
Let $u=x$
$\quad v=\cos(\sqrt 3x)$
$u'=1$
$v'=-\sin(\sqrt 3x).\sqrt 3$
Step 2:
$\therefore \large\frac{dy}{dx}$$=x.(-\sin(\sqrt 3x).\sqrt 3)+\cos (\sqrt 3x).1$
$\qquad=\cos(\sqrt 3x)-x\sqrt 3.\sin(\sqrt 3x)$
answered Sep 27, 2013 by sreemathi.v
 
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