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, derivative of cosec x using first principle, -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.

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. The resultant of the derivative of cosec x is -cot x cosec x.

Derivative of cosec x using first principle

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Now, to evaluate the derivative of csc x using the chain rule, we will use certain trigonometric properties and identities such as:.

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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.

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. We use the existing trigonometric identities and existing rules of differentiation to prove the derivative of cosec x to be -cot x cosec x. Now, we will derive the derivative of cosec x by the first principle of derivatives, that is, the definition of limits.

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Save Article. Enhance the article with your expertise. What is the integral of cosec x? Report issue Report. Like Article Like. Already booked a tutor? The derivative of cosec x is the rate of change with respect to the angle i. Maths Questions. Learn Practice Download. Derivative of the function is defined as the rate of change of the function with respect to a variable. Share your thoughts in the comments.

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.

We are going to use certain trigonometry formulas to determine the derivative of csc x. Admission Experiences. Vote for difficulty :. Article Tags :. Last Updated : 30 Jan, Our Team. Engineering Exam Experiences. Save Article. Like Article. Maths Program. To determine the second derivative of cosec x, we differentiate -cosec x cot x using the product rule. Create Improvement.