# Thread: Another Second Derivative question

1. ## Another Second Derivative question

Find $f''(x)$ if $f(x)=4e^{7x^4}$

Heres my work but I think its wrong b/c I cant finish it

$f'(x)=4e^{7x^4}(28x^3)$

$=112x^3e^{7x^4}$

$f''(x)=112x^3e^{7x^4}(28x^3)+e^{7x^4}(336x^2)$

2. Originally Posted by McDiesel
Find $f''(x)$ if $f(x)=4e^{7x^4}$

Heres my work but I think its wrong b/c I cant finish it

$f'(x)=4e^{7x^4}(28x^3)$

$=112x^3e^{7x^4}$

$f''(x)=112x^3e^{7x^4}(28x^3)+e^{7x^4}(336x^2)$
you are right so far. now just simplify

3. $f''(x)=112x^3e^{7x^4}(28x^3)+e^{7x^4}(336x^2)$

$f''(x)=3136x^6e^{7x^4}+336x^2e^{7x^4}$

Yes/no?

4. Yes, that's correct . You can factorise if you wish!

$f"(x) = 16x^{2}e^{7x^{4}}\ (196x^{4} + 21)$

I hope that helps.

ILoveMaths07.