Updated By SaraNextGen

On March 11, 2024, 11:35 AM

Question 1:

Differentiate the following w.r.t. x:

Answer:

Let

By using the quotient rule, we obtain

Question 2:

Differentiate the following w.r.t. x:

Answer:

Let

By using the chain rule, we obtain

Question 3:

Differentiate the following w.r.t. x:

Answer:

Let 

By using the chain rule, we obtain

Question 4:

Differentiate the following w.r.t. x:

Answer:

Let

By using the chain rule, we obtain

Question 5:

Differentiate the following w.r.t. x:

Answer:

Let

By using the chain rule, we obtain

Question 6:

Differentiate the following w.r.t. x:

Answer:

Question 7:

Differentiate the following w.r.t. x:

Answer:

Let

Then, 

By differentiating this relationship with respect to x, we obtain

Question 8:

Differentiate the following w.r.t. x:

Answer:

Let

By using the chain rule, we obtain

, x > 1

Question 9:

Differentiate the following w.r.t. x:

Answer:

Let

By using the quotient rule, we obtain

Question 10:

Differentiate the following w.r.t. x:

Answer:

Let

By using the chain rule, we obtain