Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): cosec x cot x

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Solution

Let

By Leibnitz product rule,

By first principle,

Now, let f₂(x) = cosec x. Accordingly,

By first principle,

From (1), (2), and (3), we obtain

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Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): cosec x cot x

Let By Leibnitz product rule, By first principle, Now, let f2(x) = cosec x. Accordingly, By first principle, From (1), (2), and (3), we obtain

Let

By Leibnitz product rule,

By first principle,

Now, let f₂(x) = cosec x. Accordingly,

By first principle,

From (1), (2), and (3), we obtain