Apply the product rule: 

Then apply the product rule  (where "n" is the exponent) where needed.

Apply the product rule: 

Then apply the product rule  (where "n" is the exponent) where needed.

Apply the product rule: 

Tek the derivative of the function using the power rule   (where "n" is the exponent) on the original function then multiply that by the derivative with respect to "x" again using the power rule:

To find the inflection point of a fuction, one needs to find the x-value where the second derivative of a function changes its sign. At the inflection point, the second derivative is either equal to zero or DNE (does not exist). In this example, the function's and its second derivative's domain is all real numbers, thus, one needs to find x-value where the second derivative is equal to zero.

The first derivative of the the function can be found using the power rule, product rule, and exponential rule.

Power Rule: 

Product Rule: 

Exponential Rule: 

Applying these rules on our equation we find the derivative to be as follows.

, is  

The second derivative of the function is

Now, set the , and solve for the x-value.

The answer is .

To find the y-component of the inflection point, plug  into the original function f, and .

Thus, the inflection point is .

To find the second derivative, you must first find the first derivative of the function.

Remember, to take the derivative, you multiply the exponent of a term by the coefficient in front of that term and then decrease the exponent by 1 (this is known as the power rule).

Therefore, the first derivative is:

.

Then, take the derivative of that function again applying the power rule so that you get the second derivative:

.

To take the derivative, multiply the exponent by the coefficient in front of the x and then subtract the exponent by 1.

Constants have a derivative of 0.

Look at each term separately and then link together at the end.

The derivative of is .

The derivative of is .

The derivative of is 4.

Remember, has a derivative of zero.

Then, link them all together:

.

To find the derivative of , we'll make use of the chain rule and product rule of derivatives. Starting with the product rule:

Now to find these two new derivatives, utilize the chain rule:

Putting this all together gives:

To perform this derivative, make use of the chain rule. The derivative of a natural log function follows the form:

 Where  designates a derivative:

So for the function

The derivative can be expressed as:

That takes care of the outer most natural log term; now all that remains is to differentiate the function in the numerator:

For the function

It will be useful to utilize both the chain rule and quotient rule. Let's begin by writing out the form of the equation using the quotient rule:

Note that  is being used to denote derivatives. Now that we have a form of what our derivative looks like, let's address the  and  terms.

The first term is simply

However, the second term will require use of the chain rule:

Now that the derivative terms are known, they can all be put together: