To differentiate the function with respect to , you use the product rule.

The product rule states that if you have a function of the form , the derivative is given by:

.

In this case, let and .

Now, we’ll find their derivatives:

(using the power rule).

To find , we’ll need to use the chain rule. The chain rule states that if you have a composite function, such as , the derivative of with respect to is given by:

.

Let , so . Now, we can find :

.

(the derivative of is , and the derivative of a constant, , is ).

So,

.

Now, we can apply the product rule:

.

Now, simplify this expression:

.

So, the corrected derivative of with respect to is:

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This answer was edited.To differentiate the function with respect to , you use the product rule.

The product rule states that if you have a function of the form , the derivative is given by:

.

In this case, let and .

Now, we’ll find their derivatives:

(using the power rule).

To find , we’ll need to use the chain rule. The chain rule states that if you have a composite function, such as , the derivative of with respect to is given by:

.

Let , so . Now, we can find :

.

(the derivative of is , and the derivative of a constant, , is ).

So,

.

Now, we can apply the product rule:

.

Now, simplify this expression:

.

So, the corrected derivative of with respect to is:

.