# Troubleshooting Product and Chain Rule for h(t) Derivatives

• Rasine
In summary, when finding the derivative of h(t)=(t^6-1)^5(t^5+1)^6, it is important to correctly apply the product rule and chain rule. While the factors (t^6-1)^4(t^5+1)^6 and (t^5+1)^5(t^6-1)^5 are correct, the factors involving a power of t should be 30t^5(t^6-1)^4 and 30t^4(t^5+1)^5. Paying attention to these details will result in the correct derivative of h'(t)."

#### Rasine

i am having trouble with this one problem. maybe you can tell me where i am going wrong.

find h'(t) if h(t)=(t^6-1)^5(t^5+1)^6

so i am using product rule and to find the derivatives of each expression i am using chain rule...

so i get h'(t)=30t^4(t^6-1)^4(t^5+1)^6+30^4(t^5+1)^5(t^6-1)^5

is that right..or what is wrong with it?

Not quite right. The factors $(t^6-1)^4(t^5+1)^6$ and $(t^5+1)^5(t^6-1)^5$ in the two terms are correct, but the factors involving a power of $t$ are not.

What is $\frac d{dt}\left((t^6-1)^5\right)$ ?

Rasine said:
i am having trouble with this one problem. maybe you can tell me where i am going wrong.

find h'(t) if h(t)=(t^6-1)^5(t^5+1)^6

so i am using product rule and to find the derivatives of each expression i am using chain rule...

so i get h'(t)=30t^4(t^6-1)^4(t^5+1)^6+30^4(t^5+1)^5(t^6-1)^5

is that right..or what is wrong with it?
The derivative of (t6-1)5 is 5(t6-1)4(6t5= 30t5(t6-1)4. I think you've missed a power of t in the first term above.

The derivative of (t5+ 1)6 is 6(t5+ 1)5(5t4)= 30t4(t5+ 1)5
You seem to be missing a "t"! (30^4 instead of 30t^4!)

## What is the purpose of troubleshooting product and chain rule for h(t) derivatives?

The purpose of troubleshooting product and chain rule for h(t) derivatives is to identify and fix errors or issues that may arise when using these mathematical rules to find the derivative of a function. These rules can be complex and may require troubleshooting in order to accurately calculate the derivative.

## What is the product rule for finding the derivative of a function?

The product rule is a mathematical rule used to find the derivative of a product of two functions. It states that the derivative of the product of two functions is equal to the first function times the derivative of the second function, plus the second function times the derivative of the first function.

## What is the chain rule for finding the derivative of a function?

The chain rule is a mathematical rule used to find the derivative of a composite function, which is a function that is made up of two or more functions. It states that the derivative of a composite function is equal to the derivative of the outer function evaluated at the inner function, times the derivative of the inner function.

## What are some common mistakes when using the product and chain rule for h(t) derivatives?

Some common mistakes when using the product and chain rule for h(t) derivatives include forgetting to apply the rules correctly, not simplifying the final answer, and making errors in algebraic calculations. It is important to carefully follow the rules and double check all calculations to avoid these mistakes.

## How can I effectively troubleshoot errors when using the product and chain rule for h(t) derivatives?

To effectively troubleshoot errors when using the product and chain rule for h(t) derivatives, it is helpful to carefully review the rules and make sure they are being applied correctly. It is also important to double check all calculations and use algebraic simplification to avoid errors. Additionally, seeking help from a tutor or professor can be beneficial in identifying and fixing any issues.