Question

Differentiate $y=\text{cosec}x\cot x$ w.r.t $x$

• A. $\text{cosec}x({\text{cosec}}^{2}x+{\cot }^{2}x)$
• B. $\text{cosec}x$
• C. $-\text{cosec}x({\text{cosec}}^{2}x+{\cot }^{2}x)$
• D. $\text{cosec}x({\text{cosec}}^{2}x-{\cot }^{2}x)$

Answer 1

The correct option is C $-\text{cosec}x({\text{cosec}}^{2}x+{\cot }^{2}x)$

Given $y=f\left(x\right)=\text{cosec x}\cot x$
By using multiplication rule derivative is given as
$f^{{}^{\prime }}\left(x\right)=\text{cosec x}(\cot x{)}^{{}^{\prime }}+(\text{cosec}x{)}^{{}^{\prime }}\cot x$
$=\text{cosec}x(-{\text{cosec}}^{2}x)+(-\text{cosec}x\cot x)\cot x$
$=-\text{cosec}x({\text{cosec}}^{2}x+{\cot }^{2}x)$