## anonymous one year ago How do you apply the power rule when E is raised by an power to a power? f[x] = e^(x^2) f'[x] = ???

1. TheSmartOne

@Michele_Laino QH help :)

2. amistre64

derivative or integration?

3. mathstudent55

You don;t use the power rule here. Here you need the derivative of e^u, where u is a function in x.

4. amistre64

i see, derivative, chain and then power

5. anonymous

trying to get to derivative.. yes

6. mathstudent55

$$\dfrac{d}{dx} e^u = e^u \dfrac{d}{dx}u$$

7. Michele_Laino

here we have to apply the derivation of composed functions

8. mathstudent55

Oh, I see. The power rule does come in to differentiate the exponent, x^2.

9. anonymous

so its like 2 functions?

10. Michele_Laino

noe we can write your function as follows: $f\left( x \right) = {e^{g\left( x \right)}},\quad g\left( x \right) = {x^2}$

11. Michele_Laino

so the requested first derivative is given by the subsequent formula: $f'\left( x \right) = \frac{{df}}{{dg}} \times \frac{{dg}}{{dx}} = {e^{g\left( x \right)}} \times 2x = 2x{e^{{x^2}}}$

12. anonymous

wicked .. thank you now I just need to get my head around that.. :) ... first day solving derivative problems using rules. .. :)

13. Michele_Laino

thank you! :)

14. anonymous

makes sense though :)

15. Michele_Laino

need more help?

16. anonymous

all good thnx

17. Michele_Laino

thanks!! :)