Derivative of cosec x using first principle

The derivative of cosec x is negative of the product of trigonometric functions cosec x and cot x, that is, -cosec x cot x. The differentiation of csc x is the process of evaluating the derivative of cosec x with respect to angle x. Before proving the differentiation of cosec x, let us recall the derivative of cosec x using first principle of cosec x also written as csc x.

Cosecant Functions are denoted as csc or cosec and defined as the reciprocal of the sine function i. In this article, we will discuss all the topics related to the derivative of cosec x including its proof using various methods. Among the trig derivatives, the derivative of the cosec x is one of the derivatives. The derivative of the cosec x is -cot x cosec x. The derivative of cosec x is the rate of change with respect to the angle i.

Derivative of cosec x using first principle

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Last Updated : 30 Jan, Like Article Like.

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The derivative of cosecant function with respect to a variable is equal to the negative product of cosecant and cotangent. The derivative of cosecant function is derived mathematically from first principle. For simplifying the difference of the cosecant functions in the numerator, express each cosecant function in terms of sine function as per reciprocal identity of sin function. In numerator, two sine functions are subtracting. The difference of them can be simplified by using difference of sine functions to product transforming trigonometric identity. Use product rule of limits to find the limit of product of functions by the product of their limits. So, shift it to denominator. Firstly, evaluate the first factor by using direct substitution method and do not touch the second factor at this time.

Derivative of cosec x using first principle

The derivative of cosec x is negative of the product of trigonometric functions cosec x and cot x, that is, -cosec x cot x. The differentiation of csc x is the process of evaluating the derivative of cosec x with respect to angle x. Before proving the differentiation of cosec x, let us recall the definition of cosec x also written as csc x. Cosec x is the ratio of the hypotenuse and the perpendicular sides of a right-angled triangle. Let us understand the differentiation of cosec x along with its proof in different methods such as the first principle of derivatives, chain rule, quotient rule, and also we will solve a few examples using the derivative of cosec x. Derivative of cosec x can be calculated using the derivative of sin x. The differentiation of cosec x can be done in different ways. The derivative of cosec x can be derived using the definition of the limit, chain rule, and quotient rule.

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Like Article. Help us improve. Maths Program. Example 2: Determine the second derivative of cosec x. Engineering Exam Experiences. Our Team. Similar Reads. You will be notified via email once the article is available for improvement. The formulas are:. The differentiation of cosec x can be done in different ways. The resultant of the derivative of cosec x is -cot x cosec x. Already booked a tutor? About Us. Privacy Policy. Share your thoughts in the comments.

Cosecant Functions are denoted as csc or cosec and defined as the reciprocal of the sine function i.

Share your thoughts in the comments. Now, to evaluate the derivative of csc x using the chain rule, we will use certain trigonometric properties and identities such as:. What kind of Experience do you want to share? Maths Program. Admission Experiences. Interview Experiences. Derivative of Cosec x. Previous Derivative Rules. Change Language. Like Article Like. Practice Questions on Derivative of Cosec x. Maths Games. Multiplication Tables. Statistics Cheat Sheet. The differentiation of a trigonometric function is called a derivative of the trigonometric function or trig derivatives.