Derivative help and specific problem

[biochem850]

Homework Statement

Find derivative of (x^2+1)^2*(x^3-2x)^2

Homework Equations

This is globally a product and you would use the power rule as well as the product rule.

The Attempt at a Solution

[(x^2+1)^2*2(x^3-2x)*3x^2-2]+[(x^3-2x)^2*2(x^2+1)*2x]

I believe I'm correct but I simply cannot simplify my answer. In addition, what would you recommend someone should do if they wanted to become proficient in taking derivatives (I've always liked math and physics and I'm considering changing my major to physics so I'd need to be proficient in derivatives).

 

[LCKurtz]

Homework Statement

Find derivative of (x^2+1)^2*(x^3-2x)^2

Homework Equations

This is globally a product and you would use the power rule as well as the product rule.

The Attempt at a Solution

[(x^2+1)^2*2(x^3-2x)*(3x^2-2)]+[(x^3-2x)^2*2(x^2+1)*2x]

I believe I'm correct but I simply cannot simplify my answer. In addition, what would you recommend someone should do if they wanted to become proficient in taking derivatives (I've always liked math and physics and I'm considering changing my major to physics so I'd need to be proficient in derivatives).

Homework Statement

Parentheses are important. I have added some where you left them out. The key to simplifying problems like this is to factor it. Look for common factors in the two terms and factor them out and simplify it.

 

[Dick]

I think you did a fine job of taking the derivative, but I'd use a couple more paranthesis. To simplify factor out common factors of (x^2+1) and (x^3-2x) and then see if you can do anything with the rest. I think you are proficient in derivatives. I'd keep on with your current career choice.

 

[biochem850]

I think you did a fine job of taking the derivative, but I'd use a couple more paranthesis. To simplify factor out common factors of (x^2+1) and (x^3-2x) and then see if you can do anything with the rest. I think you are proficient in derivatives. I'd keep on with your current career choice.

Are you saying I should or should not pursue physics (I'm just curious)?

 

[biochem850]

I think I've got the simplified derivative:

2x(x^2+1)(x^2-2)(5x^4-3x^2-2)

I factor things out from both terms and then simplified (thanks for the parenthesis suggestion).

 

[Dick]

I think I've got the simplified derivative:

2x(x^2+1)(x^2-2)(5x^4-3x^2-2)

I factor things out from both terms and then simplified (thanks for the parenthesis suggestion).

That looks good so far. You could factor 5x^4-3x^2-2 some more if you really worked at it. But how much you want to simplify something depends on what you want to do with it. Both math and physics need derivatives and you seem to be able to do them, so a decision to switch shouldn't be based on derivatives.