Differentiation Question 220
Question: If $ y={{(x{{\cot }^{3}}x)}^{3/2}}, $ then $ dy/dx= $
Options:
A) $ \frac{3}{2}{{(x{{\cot }^{3}}x)}^{1/2}}[{{\cot }^{3}}x-3x{{\cot }^{2}}x\cos e{c^{2}}x] $
B) $ \frac{3}{2}{{(x{{\cot }^{3}}x)}^{1/2}}[{{\cot }^{2}}x-3x{{\cot }^{2}}xcose{c^{2}}x] $
C) $ \frac{3}{2}{{(x{{\cot }^{3}}x)}^{1/3}}[{{\cot }^{3}}x-3xcose{c^{2}}x] $
D) $ \frac{3}{2}{{(x{{\cot }^{3}}x)}^{3/2}}[{{\cot }^{3}}x-3xcose{c^{2}}x] $
Show Answer
Answer:
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(-cose{c^{2}}x)] $
$ =\frac{3}{2}{{(x{{\cot }^{3}}x)}^{1/2}}[{{\cot }^{3}}x-3x{{\cot }^{2}}xcose{c^{2}}x] $ .
BETA
