Derivative of f(x)=(1-x)2(1+x)3?

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In summary, in order to find the first derivative of f(x)=(1-x)^2(1+x)^3, you need to apply both the product rule and the composition rule. First, use the product rule to find f'(x) = g'(x)*h(x) + g(x)*h'(x). Then, apply the composition rule to find g'(x) and h'(x) using the power rule when needed.
  • #1
jhodzzz
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what is the first derivative of f(x)=(1-x)2(1+x)3?
 
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  • #2


You have to apply two rules here - the rule for taking the derivative of a product of functions, and the rule for taking the derivative of a composition of functions. What is the product, and what is the composition? What are the composition and product rules?
 
  • #3


you see, that's the reason why I posted this thread. I'm somehow confused on what to use. Will I use the power rule or the product rule?? if I'm going to use the power rule, i'll arrive on an answer like this: 2(1-x)*3(1+x)2

is that correct??
 
  • #4


You have to use both.

Let's say f (x) = g(x) * h(x), so g(x) = (1-x)^2 and h(x) = (1+x)^3.

First, apply the product rule, since you have a product of functions, i.e. f'(x) = g'(x)*h(x) + g(x)*h'(x).

Now you only need to apply the composition rule to sind g'(x) and h'(x).
 
  • #5


No, because you need to apply the product rule.

(fg)' is not f'g'!

The rule is:

(fg)'=f'g+fg'.

Only when you apply this rule, you can take the derivative of f and g by the power rule when needed.
 
  • #6


alright2x...got it...now I'm enlightened..thanks a lot for the help.. :)
 

1. What is the derivative of f(x)?

The derivative of f(x)=(1-x)2(1+x)3 is -10x4+16x3 -10x2+4x+5.

2. How do you find the derivative of this function?

The derivative of a function is found by using the power rule, product rule, and chain rule in calculus. In this case, we would first use the power rule to find the derivative of each term, then use the product rule to combine them.

3. What is the significance of the derivative in this function?

The derivative of a function represents the rate of change of the function at a specific point. In this case, it tells us how fast the function is changing at any given value of x.

4. How can the derivative of this function be used in real-world applications?

The derivative can be used in various fields such as physics, economics, and engineering to analyze and predict changes in a system. For example, in economics, the derivative can be used to determine the marginal cost and revenue of a company.

5. Are there any special cases or exceptions when finding the derivative of this function?

The derivative of this function follows the general rules of differentiation, but it is always important to check for any potential special cases or exceptions. In this case, we would need to ensure that the derivative exists at all points of the function and that there are no undefined or discontinuous points.

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