To find the derivative, you must first use the chain rule. The derivative of is , and you multiply that by the derivative of the exponent, which is . Putting that all together, you get the final answer as .

To find the derivative, you must first use the chain rule. The derivative of is , and you multiply that by the derivative of the exponent, which is . Putting that all together, you get the final answer as .

To find the second derivative, first one has to find the first derivative, then take the derivative of this result.

The derivative of is .

The derivative of is , and this is our final answer.

First, we should simplify the problem by distributing through the parenthesis.

.

Now, since we have a polynomial, we use the power rule to take the derivative. Multiply the coefficient by the exponent, and reduce the power by 1.

.

The derivative of the function is equal to

and was found using the following rules:

, ,

We use the product rule to differentiate this function. Applying it looks like this:

This simplifies to:

We apply the chain rule to differentiate , which becomes . Plugging this into the above equation gives us:

or

Step 1: Recall the derivative rules:

-For any term with an exponent, the exponent drops and gets multiplied to the coefficient of that term. The new exponent is one less than the original one..
-For any term in the form "ax", the derivative of this term is just the coefficient.
-For any term with no x term (constant), the derivative is always

Step 2: Take the derivative:

The first derivative of is

The derivative of the function is equal to

and was found using the following rules:

, ,

The derivative of the function is equal to

and was found using the following rules:

, ,

Evaluating the limit directly will produce an indeterminant solution of .

The limit definition of a derivative is . However, the alternative form, , better suits the given limit.

Let and notice . It follows that .

Thus, the limit is