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The derivative of the cosec x is -cosec x cot x, which is the negative of the product of the trigonometry cosec x & cot x. The procedure of assessing the derivatives of cosec x along with angle x is called the differentiation of cosec x. Let us review the concept of cosec x before establishing its differentiation. Cosec x is the ratio of a right-angled triangle’s hypotenuse and opposite sides.
d(cosec x)/dx = (cosec x)’ = -cot x cosec x is the differentiation value of cosec x with regard to angle x. The derivative of sin x can be used to determine the derivative of cosec x. Different methods can be used to differentiate cosec x. The chain rule, limit definition, and quotient rule can all be used to find the derivative of cosec x. We prove that the derivative of cosec x is -cot x cosec x using current trigonometric identities and differentiation procedures.
The derivative value of cosec x has the following formula:
- d(cosec x)/dx = -cot x cosec x
- (cosec x)’ = -cot x cosec x
Example: Calculate the cosec x cot x derivative.
The product rule can be used to find the derivative valuation of cosec x cot x. We know d(cosec x)/dx = -cot x cosec x, and d(cot x)/dx = -cosec2x.
We have used the product rule to find,
d(cosec x cot x)/dx = (cosec x cot x)’
(cosec x)’ cot x + cosec x (cot x)’ = -cosec x cot x cot x + cosec x (-cosec2x) = -cosec x (cot2x + cosec2x)
Therefore the Answer will be, -csc x (cot2x + csc2x) is the derivative of cosec x cot x.
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