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Commutative Law of Binary Operation

Find the deri...

Question

Find the derivative of the following functions from first principle:

(i) –x (ii) (–x)^–1 (iii) sin (x + 1)

(iv)

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Solution

(i) Let f(x) = –x. Accordingly,

By first principle,

(ii) Let. Accordingly,

By first principle,

(iii) Let f(x) = sin (x + 1). Accordingly,

By first principle,

(iv) Let. Accordingly,

By first principle,

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