How do you differentiate given $y = 2x (x^(1/2) - cot x)$ ?

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Answer 1 · 2016-06-03T09:58:25

$=frac{2x+3sqrt{x}sin ^2(x)-2sin ^2(x)cot (x)}{sin ^2(x)}$

$frac{d}{dx}(2x(sqrt{x}-cot (x)))$

Taking the constant out,
$(a\cdot f)^'=a\cdot f^'$

$=2frac{d}{dx}(x(sqrt{x}-cot (x)))$

Applying the product rule,
$(fcdot g)^'=f^'cdot g+fcdot g^'$
$f=x:g=sqrtx -cotx$

$=2(frac{d}{dx}(x)(sqrt{x}-cot(x))+frac{d}{dx}(sqrt{x}-cot (x))x)$

We know,
$frac{d}{dx}(x)=1$

$frac{d}{dx}(sqrt{x}-cot(x))=frac{1}{2sqrt{x}}+frac{1}{sin ^2(x)}$

$=2(1(sqrt{x}-\cot (x))+(frac{1}{2sqrt{x}}+frac{1}{sin ^2(x)})x)$

Simplify,
$=frac{2x+3sqrt{x}sin ^2(x)-2sin ^2(x)cot (x)}{sin ^2(x)}$

How do you differentiate given y = 2x (x^(1/2) - cot x)y = 2x (x^(1/2) - cot x)?