integral and derivative help (1 Viewer)

[survivor]

whats the answer to....
1.) d(ln(x/x^2+1)/dx????

2.) integral of (x^2 times e^-x^3)

3.)integral of (e^x - ex)???

4.)d(x^2ln(x/2))/dx??

please if you can do any it would be much appreaciated...

thankyou

 

[kini mini]

How much calculus have you done? These are basic questions, especially for this time of year . I would prefer that you work the questions out using my hints or ask questions about calculus in general, if you can't do these you're in a bit of strife I'm afraid. If you are really stuck post again or PM me.

Originally posted by survivor
whats the answer to....
1.) d(ln(x/x^2+1)/dx????

You need the chain rule and then quotient rule here.

To start you off - d/dx of (ln(x/x^2 + 1) = [(x^2 + 1)/x]* d/dx(x/x^2 +1)

2.) integral of (x^2 times e^-x^3)

Think about the primitive of that expression - it must differentiate to make (x^2 times e^-x^3)...

3.)integral of (e^x - ex)???

The derivative of e^x is e^x. e is a constant. Does that help?

4.)d(x^2ln(x/2))/dx??

Chain rule.

 

[underthesun]

but if he's still year 11, then it's ok

btw, for question one,

ln(x / x² + 1) = lnx - ln(x² + 1)

right?

then it's easy to differentiate.

 

[kini mini]

Originally posted by underthesun
but if he's still year 11, then it's ok

Ah that makes sense

btw, for question one,

ln(x / x² + 1) = lnx - ln(x² + 1)

right?

then it's easy to differentiate.

Hehe quite right, that's easier .