Please show me how you would solve this problem so that I can compare with mine...Thxs so much...I need to finish this asap...
Thxs so much for ur help
the second last step...that's the part I am not how I can simplyfy to get that polynomial Pk(x)
I have tried many ways...but I can't seem to get the proving right...
Could you please show me your workings so I can check with mine?
Thxs
Hiya,
Thxs for the prompt reply...
I have done this d^(k+1)/dx^(K+1) (e^(x^2) = d/dx(d^k/dx^k (e^x^2)
= (Pk (x). e^(x^2)
Then I used product rule for this part which ended up with...
I have started the prove with n = 1, that part was okay, I managed to prove that it is true for n = 1.
The part I am having trouble with is to prove n = k+1.
For that part, I tried to use product rule to differentiate d/dx(d^k/dx^k(e^x2)
I got 2^(k+1)x^(k+1) e^x2 + e^x2(k2^kx^k-1)...
Prove by induction that for all n≥ 1,
dn/ dxn (e ^(x2) = Pn (x) e ^(x2)
where Pn(x) is a polynomial in x of degree n with coefficient of x^n equal to 2^n
I have problems trying to prove this question by mathematical induction. Please help...Really much appreciated