## Derivatives part 14: IITJEE maths tutorial problems for practice

This is part 14 of the series

Question 1:

Let for be a real valued function. Then, find for :

Answer 1:

Consider so that we have

Hence, when

Hence,

Question 2:

Let , then find .

Answer 2:

Given that ….call this I.

Also, from above, we get …call this II.

so we get ….call this I’

and …call this II’.

and hence,

Also, again ….A

…B

So, we now we get the following two equations:

…..A’

….B’

so, now we have so that we get and

so

Question 3:

If and , then find .

Answer 3:

Given that where a is a parameter (constant) and t is a variable.

Let so that

so that

so that we have

Question 4:

If then find

Answer 4:

Given that and put

so that

which is the required answer.

Question 5:

If , where a is a parameter, then find .

Answer 5:

Given that so that

Differentiating both sides w.r.t. x, we get

Question 6:

If then find .

Answer 6:

Given that so that where so that

and

Let so that

Now, note that so we get the following simplification:

Now,

Cheers,

Nalin Pithwa

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