What is the derivative of cosec x? Simple Term Explanation
A key idea in calculus is what is the derivative of cosec x?, which is a basic trigonometric function. We can improve our understanding of mathematical concepts by investigating its definition and applications.
What is the derivative of cosec x?
The product of the trigonometry cosec x & cot x is -cosec x cot x, which is the derivative of the cosec x. Differentiation of cosec x is the process of evaluating the derivatives of cosec x in conjunction with angle x. Before we differentiate cosec x, let’s go over the idea in brief. The ratio of the hypotenuse to the opposite sides of a right-angled triangle is cosec x.
(Cosec x)’ = -cot x = d(cosec x)/dx The differentiation value of cosec x with respect to angle x is cosec x. One can find the derivative of cosec x by using the derivative of sin x. Different techniques can be applied to distinguish cosec x. The derivative of cosec x can be found using the quotient rule, chain rule, and limit definition. Using the most recent trigonometric identities and differentiation techniques, we demonstrate that the derivative of cosec x is -cot x cosec x.
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The following formula represents the derivative value of cosec x:
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.