I am not able to find the derivative of the following function by first principle. I need the entire procedure of the first principle. Thanx in advance.

f(x)= x^2.cosx

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- September 12th 2008, 12:56 PMtariq_h_tauheedDeivative by first principle.
I am not able to find the derivative of the following function by first principle. I need the entire procedure of the first principle. Thanx in advance.

*f(x)= x^2*.*cosx* - September 12th 2008, 01:03 PMarbolis
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Put so .

Put so . I let you finish this, it's just 2 multiplications and an addition.

EDIT: Oops... sorry I didn't know what what the "first principle". - September 12th 2008, 01:08 PMguangzhao
You can differentiate using the chain rule.

Use the identity e^(x^2)=2e^x

so e^y=2e^(x.cosx)

Differentiating,

e^y(dy/dx)=2(cosx+(-xsinx))e^(x.cosx)

Then just move e^y over and sub it as e^(x^2.cosx) - September 12th 2008, 01:08 PMtopsquark