Simplify derivative after using product and chain rule

In summary, the student attempted to simplify the derivative using the Chain Rule and Power Rule, but was not able to arrive at the correct solution. They believe they may have made a mistake with a minus sign and are seeking further assistance.
  • #1
biochem850
51
0

Homework Statement



(x[itex]^{2}[/itex]-x[itex]^{-1}[/itex]+1)(x[itex]^{3}[/itex]+2x-6)[itex]^{7}[/itex]

Homework Equations


Chain Rule & Power Rule

The Attempt at a Solution



(x[itex]^{3}[/itex]+2x-6)[itex]^{6}[/itex][(x[itex]^{3}[/itex]+2x-6)(2x+x[itex]^{-2}[/itex])+7(3x[itex]^{2}[/itex]+2)(x[itex]^{2}[/itex]-x[itex]^{-1}[/itex]+1)]

This is the farthest I've gotten but when I do additional computation I do not arrive at the correct simplified solution.

edit- should be "simplify derivative after using power rule and chain rule"

Homework Statement

Homework Equations


The Attempt at a Solution


Homework Statement


Homework Equations


The Attempt at a Solution


Homework Statement


Homework Equations


The Attempt at a Solution


Homework Statement


Homework Equations


The Attempt at a Solution


Homework Statement


Homework Equations


The Attempt at a Solution

 
Physics news on Phys.org
  • #2
hi biochem850! :wink:

looks ok so far :smile:

you've probably made a mistake with a minus somewhere later …

check them first …

if that doesn't help, then show us what you did​
 

Related to Simplify derivative after using product and chain rule

1. How do you simplify a derivative after using the product and chain rule?

To simplify a derivative after using the product and chain rule, you will need to use the product rule and chain rule to find the derivative of the function. Then, you can combine like terms and simplify the resulting expression to make it easier to understand.

2. What is the product rule and how is it used in finding derivatives?

The product rule is a formula 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.

3. How does the chain rule work in finding derivatives?

The chain rule is a formula used to find the derivative of a composition of two or more functions. It states that the derivative of a composition of functions is equal to the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function.

4. Can the product and chain rule be used together to find derivatives?

Yes, the product and chain rule can be used together to find the derivative of a function that involves both products and compositions of functions. The product rule is applied first, followed by the chain rule on the resulting expression.

5. Are there any tips for simplifying derivatives after using the product and chain rule?

One tip for simplifying derivatives after using the product and chain rule is to carefully distribute and combine like terms. It can also be helpful to factor out common factors and use algebraic simplification techniques. Additionally, it may be useful to double check your work and simplify further if possible.

Similar threads

Solve the given differential equation
    • Calculus and Beyond Homework Help
Replies
10
Views
1K
Why Is the Chain Rule Not Used in Differentiating h(x) = 3f(x) + 8g(x)?
    • Calculus and Beyond Homework Help
Replies
2
Views
964
Derivatives and the chain rule
    • Calculus and Beyond Homework Help
Replies
5
Views
999
Differentiating a a rational function
    • Calculus and Beyond Homework Help
Replies
3
Views
1K
Is this a typo? Using Chain Rule and Product Rule
    • Calculus and Beyond Homework Help
Replies
2
Views
934
Problem in applying the Chain Rule
    • Calculus and Beyond Homework Help
Replies
3
Views
1K
Question on Two Differentiation Techniques
    • Calculus and Beyond Homework Help
Replies
25
Views
425
Derivative of two polynomials, one of them being squared
    • Calculus and Beyond Homework Help
Replies
18
Views
2K
Value of an implicit derivative
    • Calculus and Beyond Homework Help
Replies
4
Views
1K
Simplifying this derivative....
    • Calculus and Beyond Homework Help
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top