frac{d}{d x}left[left(x^{frac{5}{2}}-x^{frac{ | vedclass

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Question

(A) Let $u = x^{\frac{5}{2}}-x^{\frac{3}{2}}+1$ and $v = x^2-3 x+5$. Using the product rule $\frac{d}{dx}(uv) = u'v + uv'$:$u' = \frac{5}{2} x^{\frac{

Vedclass · Accepted Answer

$\frac{9}{2} x^{\frac{7}{2}}-14 x^{\frac{5}{2}}+20 x^{\frac{3}{2}}-\frac{15}{2} x^{\frac{1}{2}}+2 x-3$

Vedclass · Answer

(A) Let $u = x^{\frac{5}{2}}-x^{\frac{3}{2}}+1$ and $v = x^2-3 x+5$. Using the product rule $\frac{d}{dx}(uv) = u'v + uv'$:$u' = \frac{5}{2} x^{\frac{3}{2}}-\frac{3}{2} x^{\frac{1}{2}}$$v' = 2x-3$$\frac{d}{dx}(uv) = (\frac{5}{2} x^{\frac{3}{2}}-\frac{3}{2} x^{\frac{1}{2}})(x^2-3 x+5) + (x^{\frac{5}{2}}-x^{\frac{3}{2}}+1)(2 x-3)$$= (\frac{5}{2} x^{\frac{7}{2}} - \frac{15}{2} x^{\frac{5}{2}} + \frac{25}{2} x^{\frac{3}{2}} - \frac{3}{2} x^{\frac{5}{2}} + \frac{9}{2} x^{\frac{3}{2}} - \frac{15}{2} x^{\frac{1}{2}}) + (2 x^{\frac{7}{2}} - 3 x^{\frac{5}{2}} - 2 x^{\frac{5}{2}} + 3 x^{\frac{3}{2}} + 2 x - 3)$$= (\frac{5}{2} + 2) x^{\frac{7}{2}} + (-\frac{15}{2} - \frac{3}{2} - 3 - 2) x^{\frac{5}{2}} + (\frac{25}{2} + \frac{9}{2} + 3) x^{\frac{3}{2}} - \frac{15}{2} x^{\frac{1}{2}} + 2 x - 3$$= \frac{9}{2} x^{\frac{7}{2}} - 14 x^{\frac{5}{2}} + 20 x^{\frac{3}{2}} - \frac{15}{2} x^{\frac{1}{2}} + 2 x - 3$

$\frac{d}{d x}\left[\left(x^{\frac{5}{2}}-x^{\frac{3}{2}}+1\right)\left(x^2-3 x+5\right)\right]=$

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