# Beginner having trouble taking derivative

• Heinz21
In summary, the conversation is about difficulty in taking the derivative of functions using the chain rule and product rule together. The example given is g(x)=(1+4x)5(3+x-x2)8 and how to find g'(x) using the product rule and chain rule. The person is advised to use the product rule first and then apply the chain rule for each derivative.
Heinz21
Hello, i am having trouble taking the derivative of functions with using the chain rule plus another rule such as the product rule... i know how to do chain rule by it self and product rule by itself but i am having trouble using them together.. here is an example
g(x)= ( 1+4x )5 ( 3+x-x2 )8

Let f(x)=(1+4x)5 and h(x)=(3+x-x2)8

The g(x)=f(x)h(x) and g'(x)=f(x)h'(x) + f'(x)h(x)

Can you do the rest yourself?

What Mathman is saying is that you first must use The Product Rule for Differentiation.
Then each derivative [h ' (x) and f ' (x) ] will require using The Chain Rule.

## 1. How do I take the derivative of a function?

To take the derivative of a function, you need to use the rules of differentiation, such as the power rule, product rule, and chain rule. You can also use online calculators or software to help you find the derivative.

## 2. What is the purpose of taking a derivative?

The derivative is used to find the rate of change of a function at a specific point. It can also be used to find the slope of a tangent line to a curve, or to optimize functions in calculus problems.

## 3. What are common mistakes beginners make when taking derivatives?

Some common mistakes include forgetting to apply the chain rule, not simplifying expressions before taking the derivative, and mixing up the power rule and quotient rule. It is important to carefully follow the rules of differentiation to avoid these mistakes.

## 4. How can I improve my understanding of taking derivatives?

Practice is key to improving your understanding of taking derivatives. Make sure to work through lots of examples and try to understand the concepts behind the rules of differentiation. Seeking help from a teacher or tutor can also be beneficial.

## 5. What are some real-world applications of taking derivatives?

Taking derivatives has many real-world applications, such as in physics for calculating velocity and acceleration, in economics for maximizing profits and minimizing costs, and in engineering for optimizing the design of structures and systems.

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