sorry to bother everyone but i found a question to which i never learned process so i wonder if anyone can tell me da rules or explain it to me

 

 

[math]f(x)=e^{2x)[/math] find [math]f^6(0)[/math]

 

though i think this is a fundamental technique I must have missed it when they were teaching it. so i checked the book and it said the answer was 64

 

now the only way i could get it to equal that, is to find the derivative

 

[math]\frac{dy}{dx}=2e^{2x}[/math]

 

then solve f(0)

 

[math]f(0)=2[/math]

 

then i thought that [math]f^6(0)=(f(0))^6[/math]

 

so i did [math]2^6=64[/math]

 

i'm not sure if my process is right (which i think it isn't cuz it didn't say

[math](f^6(0))'[/math])

 

someone please explain

 

thx

Your process isn't right, but your answer is. The nth derivative of e^2x is 2ⁿe^2x. Using that, just plug in n=6 and you get 2⁶=64.

oh ok

[math]f(x)=e^{2x)[/math] find [math]f^6(0)[/math]

 

When you have [math]f^6(0)[/math] this means the 6th derivative of f. It is actually more commonly written as [math]f^{(6)}(0)[/math] to show that it is a derivative of f as opposed to a power of f.

thank you