Derivative Help: differentiate using product rule

That's where the product rule comes in.In summary, the conversation discusses finding the derivative of a product of two functions, f(x) and g(x), using the product rule. It is mentioned that the derivative of f(x) is -6x^3+2x and the derivative of g(x) is -1/x^4. The conversation also mentions that the product rule is used to find the derivative and there is a mistake in the result for g'(x) and f'(x)g(x).
  • #1
digidako
6
0

Homework Statement



(1-2x3+x2)((1/x3)+1)

Homework Equations



f'g(x)+g'f(x)
f'(x)=-6x3+2x
g'(x)=(-1/x4)

The Attempt at a Solution



I found what i believe to be the derivative of both f(x) & g(x) and used the product rule to get to where I am stuck right now:

[(-6x2+2x)(1/x3)]+[(-1/x4)(1-2x3+x2)
 
Last edited:
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  • #2
digidako said:

Homework Statement



(1-2x3+x2)((1/x3)+1)

Homework Equations



f'g(x)+g'f(x)
f'(x)=-6x3+2x
g'(x)=(-1/x4)

The Attempt at a Solution



I found what i believe to be the derivative of both f(x) & g(x) and used the product rule to get to where I am stuck right now:

[(-6x2+2x)(1/x3)]+[(-1/x4)(1-2x3+x2)
Your result for g'(x) is wrong, assuming that g(x)=1/x3+1. Your f'(x)g(x) is wrong too.
 

What is the product rule for differentiation?

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

When should I use the product rule for differentiation?

You should use the product rule when you need to find the derivative of a product of two functions. This is a common situation in calculus problems involving finding the rate of change of a quantity that is dependent on two variables.

Can I use the product rule for differentiation for more than two functions?

No, the product rule is only applicable to two functions. If you have more than two functions in a product, you will need to use more advanced techniques such as the chain rule or the quotient rule.

How do I apply the product rule for differentiation?

To apply the product rule, simply identify the two functions in the product and their respective derivatives. Then, plug them into the formula: f'(x) = g(x) * f'(x) + f(x) * g'(x), where g(x) and f(x) are the two functions and g'(x) and f'(x) are their derivatives.

Can I use the product rule for differentiation for functions with more than one variable?

Yes, the product rule can be applied to functions with more than one variable. In this case, the derivatives of the functions will be with respect to the different variables and the product rule will still hold.

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