Final Answer
$-\csc\left(x\right)^2$
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Step-by-step Solution
Problem to solve:
$\frac{d}{dx}\left(\cos\left(x\right)\right)\cdot \csc\left(x\right)$
Choose the solving method
1
Apply the trigonometric identity: $\csc\left(x\right)\cos\left(x\right)$$=\cot\left(x\right)$
$\frac{d}{dx}\left(\cot\left(x\right)\right)$
2
Taking the derivative of cotangent
$-\csc\left(x\right)^2$
Final Answer
$-\csc\left(x\right)^2$