TS EAMCET · Maths · Differentiation
\(\frac{d}{d x}\left[\left(x^{\frac{5}{2}}-x^{\frac{3}{2}}+1\right)\left(x^2-3 x+5\right)\right]=\)
- A \(\frac{9}{2} x^{\frac{7}{2}}-14 x^{\frac{5}{2}}+20 x^{\frac{3}{2}}-\frac{15}{2} x^{\frac{1}{2}}+2 x-3\)
- B \(\frac{9}{2} x^{\frac{7}{2}}-7 x^{\frac{5}{2}}+5 x^{\frac{3}{2}}-\frac{3}{2} x^{\frac{1}{2}}+2 x-3\)
- C \(9 x^{\frac{7}{2}}-14 x^{\frac{5}{2}}+20 x^{\frac{3}{2}}-15 x^{\frac{1}{2}}+2 x-3\)
- D \(\frac{9}{2} x^{\frac{7}{2}}-\frac{7}{2} x^{\frac{5}{2}}+\frac{5}{2} x^{\frac{3}{2}}-\frac{15}{2} x^{\frac{1}{2}}+2 x-3\)
Answer & Solution
Correct Answer
(A) \(\frac{9}{2} x^{\frac{7}{2}}-14 x^{\frac{5}{2}}+20 x^{\frac{3}{2}}-\frac{15}{2} x^{\frac{1}{2}}+2 x-3\)
Step-by-step Solution
Detailed explanation
We have \(\frac{d}{d x}\left[\left(x^{\frac{5}{2}}-x^{\frac{3}{2}}+1\right)\left(x^2-3 x+5\right)\right]\)…
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