How do you differentiate $f(x)=xsinsqrtx$ using the chain rule?

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Answer 1 · 2017-03-27T23:34:13

$sinsqrtx + (cossqrtx * sqrtx)/2$

In order to differentiate $f(x) = xsinsqrtx$ , we need to use the product rule

Product rule: $f(x)*g(x) = f'(x)g(x) + g'(x)f(x)$

$f(x)*g(x) = f'(x)g(x) + g'(x)f(x)$
$x*sinsqrtx = d/dx x * sinsqrtx + d/dx sinsqrtx * x$

$x' = 1$
$sinsqrtx' = cossqrtx * d/dx sqrtx$

$1 * sinsqrtx + cossqrtx * d/dx sqrtx * x$
$sqrtx' = x^(1/2)' = (1/2)*x^((1/2) -1)= 1/(2sqrtx)$

$sinsqrtx + cossqrtx * 1/(2sqrtx) * x$
$sinsqrtx + (cossqrtx * sqrtx)/2$

How do you differentiate f(x)=xsinsqrtxf(x)=xsinsqrtx using the chain rule?