High School Math : Finding Derivative at a Point

Example Questions

Example Question #1 : Finding Derivative At A Point

Find  if the function  is given by

Explanation:

To find the derivative at , we first take the derivative of . By the derivative rule for logarithms,

Plugging in , we get

Example Question #2 : Finding Derivative At A Point

Find the derivative of the following function at the point .

Explanation:

Use the power rule on each term of the polynomial to get the derivative,

Now we plug in

Example Question #21 : Calculus I — Derivatives

Let . What is ?

Explanation:

We need to find the first derivative of f(x). This will require us to apply both the Product and Chain Rules. When we apply the Product Rule, we obtain:

In order to find the derivative of , we will need to employ the Chain Rule.

We can factor out a 2x to make this a little nicer to look at.

Now we must evaluate the derivative when x = .