Find the derivative of cot square root x using first principle. Please show your work
Solution
(
√ )
√
(
√
(√
)
(√ )
)
Indeterminate form of type 0/0. Applying L'Hospital's rule we have,
(
(√
(
(√ )
)
(√
)
(√ )
)
(
)
(√
√
(√ )
)
)
√
Thus:
(√ )
(√
)
(√
√
(
)
(√
√
)
)
√
(
√
(√
) )
√
(√
)
Answer:
(
√ )
√
√
√
√
√