Derivative of (x^2-x^-1+1)(x^3+2x-6)^7; cannot simplify

[biochem850]

Homework Statement

Find the derivative of (x^2-x^-1+1)(x^3+2x-6)^7

Homework Equations

This is a product so I used the product and chain rule where appropriate

The Attempt at a Solution

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

This is as far as I could get in my simplification. My book has an answer which is further simplified. I now that I must know combine the two bracketed factors but when I do this my answers doesn't equal my text's answer. I'm usually fine with the algebra involved in simplifying but I simply do not see where my error lies.

This is one of my first higher level math courses and I'm really trying to solidify the skills being introduced.

 

[intwo]

Your solution looks correct with the exception of missing exponents on two terms. Do you see where?

 

[biochem850]

Your solution looks correct with the exception of missing exponents on two terms. Do you see where?

My bad: (x^3+2x-6)^6[7(x^2-x^-1+1)(3x^2+2)]+[(x^3+2x-6)(2x+1/x^2)]

I don't see the other error.

 

[SammyS]

My bad: (x^3+2x-6)^6[7(x^2-x^-1+1)(3x^2+2)]+[(x^3+2x-6)(2x+1/x^2)]

I don't see the other error.

You're missing a power of 7 on the other factor of x³+2x-6, the one in the second term.

 

[intwo]

You should also have an exponent of 7.

7(x^{2} - x^{-1} +1)(x^{3}+2x - 6)^{6}(3x^{2} + 2) + (x^{3} + 2x - 6)^{7}(2x + x^{-2})

Try using the distributive property on those terms and see if you get the answer in the back of the book. I don't see any need to simplify it besides practicing algebra, but maybe some terms will cross out or something.

 

[biochem850]

You should also have an exponent of 7.

7(x^{2} - x^{-1} +1)(x^{3}+2x - 6)^{6}(3x^{2} + 2) + (x^{3} + 2x - 6)^{7}(2x + x^{-2})

Try using the distributive property on those terms and see if you get the answer in the back of the book. I don't see any need to simplify it besides practicing algebra, but maybe some terms will cross out or something.

I factored out the (x^3+2x-6)^6 and got:

(x^3+2x-6)^6[7(x^2-x^-1+1)(3x^2+2)]+[(x^3+2x-6)(2x+x^-2)]. Is this erroneous?

 

[intwo]

I factored out the (x^3+2x-6)^6 and got:

(x^3+2x-6)^6[7(x^2-x^-1+1)(3x^2+2)]+[(x^3+2x-6)(2x+x^-2)]. Is this erroneous?

Looks good. What is the answer that your book gives? You may need to multiply those terms in the brackets.

 

[biochem850]

Looks good. What is the answer that your book gives? You may need to multiply those terms in the brackets.

The text's answer:

[(x^3+2x-6)^6/x^2]* (23x^6+39x^4-32x^3+14x^2-12x-6)

 

[biochem850]

Any suggestion? I multiplied the terms in brackets and my answers is quite different from the text's.

 

[Dick]

Any suggestion? I multiplied the terms in brackets and my answers is quite different from the text's.

You are going to need to factor out an x^(-2) as well. And nobody can tell you what you did wrong until you show what you got and how you got it. And I'm going to agree with intwo. You know how to differentiate, that's clear. Spending a whole lot of time on simplification questions might not be the best use of time.