Using formal definition to find derivative

Hi

I have to find the derivative of the following function: xsinx

Using formal definition. I have tried to start this but am stuck. Can someone give me a hint to help me complete it?

What I have done so far..

lim as h approaches 0

(x+h)(sinx+h) - (xsinx)/h <---- is this correct? or have I missed something?

Re: Using formal definition to find derivative

Strictly speaking, what you have is NOT correct but only because you are missing parentheses. The derivative is given by the limit of ((x+h)sinx+h- xsinx)/h. What you wrote would be (x+y)sinx+h- (xsinx/h). Even clearer would be ((x+h)sin(x+h)- xsin(x))/h. Now I would recommend that you use "-a+ a" to isolate the changes:

((x+h)sin(x+h)- xsin(x+h)+ xsin(x+h)- xsin(x))/h and separate into (((x+h)- x)/h)sin(x)+ x((sin(x+h)- sin(x))/h.

The first you should recognise as the derivative of x and the second as the derivative of sine.

Re: Using formal definition to find derivative

Re: Using formal definition to find derivative

using the definition:

for f(x) = xsin(x), we get:

can you continue?

Re: Using formal definition to find derivative

Thank you Deveno!!!

Yes I can (Nod)

Re: Using formal definition to find derivative

Re: Using formal definition to find derivative

Quote:

Originally Posted by

**Soroban**

That's wonderful Soroban! :) But why was it slow? what happened?

Re: Using formal definition to find derivative

Apparently it took **soroban** over two hours to type his response...(Shake)(Nod)(Giggle)(Rock)(Clapping)

Re: Using formal definition to find derivative

Quote:

Originally Posted by

**MarkFL2** Apparently it took **soroban** over two hours to type his response...(Shake)(Nod)(Giggle)(Rock)(Clapping)

All those god damn brackets and parenthesis.

Re: Using formal definition to find derivative

He is the man when it comes to !!!:cool:

Re: Using formal definition to find derivative

Oh right! (Bigsmile) Thank you very much Soroban for the effort, it has helped me understand (Yes)

Re: Using formal definition to find derivative

If I was to do this using first principles, I'd evaluate the derivatives of and by first principles, then prove the product rule using first principles and apply it :)

Now as for the product rule...

So that means

Re: Using formal definition to find derivative

Quote:

Originally Posted by

**Prove It** If I was to do this using first principles, I'd evaluate the derivatives of

and

by first principles, then prove the product rule using first principles and apply it :)

Now as for the product rule...

So that means

Thank you very much for your input Prove it - much appreciated! :D