Composite Of Functions

We are given the following information:

Let's break down the expression step by step.

First, consider the term . Using the chain rule, the derivative of with respect to is:

Now, let's evaluate this at :

Since , we have:

Next, consider the term . The derivative of with respect to is:

Now, let's evaluate this at :

Since and , we have:

Finally, to find the derivative of the entire expression, we add the derivatives of the two terms:

Since , we have:

Therefore, the derivative of is 33, which corresponds to option (C) 33.

The correct answer is: (B) : 3x² + 3.

If and are two functions with and , then we are tasked with finding . Let's solve this step by step.

Step 1: Differentiate

The composition of the functions is given as . We will differentiate this expression with respect to . Using the chain rule, the derivative of is given by:

Step 2: Differentiate

The derivative of with respect to is:

Step 3: Solve for

Now, we know that the derivative of the composition of functions is:

Step 4: Find

Differentiate to find :

Step 5: Solve for

Now, using the chain rule formula , we solve for to get:

Conclusion:
Thus, the correct answer is (B) : 3x² + 3.