NCERT Class 12-Mathematics: Chapter – 5 Continuity and Differentiability Part 17 (For CBSE, ICSE, IAS, NET, NRA 2023)

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Question 55:

Answer:

We have,

By the rules given below:

Chain Rule

Product rule:

On differentiating both sides with respect to , we get

Question 56:

Answer:

We have,

On differentiating both sides with respect to , we get

Question 57:

Answer:

Question 58:

If , then show that

Answer:

Given:

Differentiating the above with respect to , we get

Now, we again differentiate with respect to y, we get

Hence Proved