Is the Product Rule the Key to Finding h'(2)?

In summary, the conversation discusses the use of the product rule to find the derivative of a function and confirms the correct application of the rule. The conversation also clarifies the use of function notation in finding a specific value of a function.
  • #1
tpcgreg
5
0
Hello,It is given that h(x) = f(x)g(x). It then tells me to write a formula for h'(2).

I know that h'(x) = f'(x)g(x) + f(x)g'(x), using the product rule.

So I assumed that h'(2) = f'(2)g(2) + f(2)g'(2)

Is this correct? Does the product rule simply allow me to do this? It seems to simple.

Thanks in advance,

Greg
 
Last edited:
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  • #2
Looks correct to me. You were expecting something really complicated?
 
  • #3
I'm in calculus 1, so this stuff is fairly new to me. Just making sure I wasn't missing something. Thanks!
 
  • #4
Yes, if a function is given by f(x)= really complicated stuff with the letter "x" in it, then
f(2)= really complicated stuff with the letter "x" replaced by the number 2.

That has nothing to do with the derivative, per se, but with "function notation".
 

FAQ: Is the Product Rule the Key to Finding h'(2)?

What is the product rule?

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

When do I use the product rule?

You would use the product rule when finding the derivative of a product of two functions, where each function is dependent on the same independent variable. This can also be applied to more than two functions, as long as they are all dependent on the same variable.

How do I apply the product rule?

The product rule can be applied by first identifying the two functions in the form of f(x) and g(x). Then, plug these functions into the formula: (f(x)*g(x))' = f'(x)*g(x) + f(x)*g'(x). Finally, simplify the expression to get the derivative of the product.

Can the product rule be used to find higher order derivatives?

Yes, the product rule can be used to find higher order derivatives by repeated application. For example, to find the second derivative of a product, you would take the derivative of the first derivative obtained from the product rule.

Are there any common mistakes when using the product rule?

One common mistake when using the product rule is forgetting to apply the rule to both functions in the product. Another mistake is incorrectly applying the power rule, which should be used separately for each function in the product before applying the product rule.

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