A) \[\frac{3}{2}{{(x{{\cot }^{3}}x)}^{1/2}}[{{\cot }^{3}}x-3x{{\cot }^{2}}x\cos \text{e}{{\text{c}}^{2}}x]\]
B) \[\frac{3}{2}{{(x{{\cot }^{3}}x)}^{1/2}}[{{\cot }^{2}}x-3x{{\cot }^{2}}x\,\text{cose}{{\text{c}}^{2}}x]\]
C) \[\frac{3}{2}{{(x{{\cot }^{3}}x)}^{1/3}}[{{\cot }^{3}}x-3x\,\text{cos}\text{e}{{\text{c}}^{2}}x]\]
D) \[\frac{3}{2}{{(x{{\cot }^{3}}x)}^{3/2}}[{{\cot }^{3}}x-3x\,\text{cos}\text{e}{{\text{c}}^{2}}x]\]
Correct Answer: A
Solution :
\[y={{(x{{\cot }^{3}}x)}^{3/2}}\] \[\therefore \frac{dy}{dx}=\frac{3}{2}{{(x{{\cot }^{3}}x)}^{1/2}}[{{\cot }^{3}}x+3x{{\cot }^{2}}x(-\text{cose}{{\text{c}}^{2}}x)]\] \[=\frac{3}{2}{{(x{{\cot }^{3}}x)}^{1/2}}[{{\cot }^{3}}x-3x{{\cot }^{2}}x\,\text{cose}{{\text{c}}^{2}}x]\].
You need to login to perform this action.
You will be redirected in
3 sec
