i dont get this...what does the e mean? what do u sustitute for e?

Question

find the value of f'(0) when
f(x)= (1/3) e^(3x) + (1/2)e^(-3x)

Answer 1

The first answerer is wrong.

f(x) = 1/3 e^(3x) + 1/2 e^(-3x)

f'(x) = 1/3 (3) e^(3x) + 1/2 (-3) e^(-3x)
f'(0) = 1/3 (3) e^(0) + 1/2 (-3) e^(0) = 1x1 + (-3/2)x1
because e^(0) = 1
so f'(0) = 1 - 3/2 = -1/2.

As for the second answerer, I don't think you can call e an exponential. e is a constant, and it belongs to a class of numbers called irrational numbers. Natural logarithms have e as its base value = 2.71828... (goes on and on and on...).

The value e can be expressed as the limit of (1 + 1/x)^x as the value of x approaches infinity.

Or it can be approximated by

1/0! + 1/1! + 1/2! + 1/3! +1/4! + 1/5! + 1/6! + ... (and so on)
= 1/1 + 1/1 +1/2 +1/6 + 1/24 + 1/120 + 1/720 + ... (and so on)

Answer 2

e= 2.71828 like pi, e is a letter representation of an irrational number.

but in this case it does not matter because if you raise it to the zero power, like any other number, it becomes 1.

f'(0) is to take the derivative then evaluate at x=0

1/3 (3e^3x) + 1/2 (-3e^(-3x))= 1 - 3/2= -1/2

Answer 3

e^x is the exponential function
e represents the number of Euler equal to 2.71828...

if f(x) = e^x then f'(x)=e^x too
if f(x) = e^(ax) then f'(x)=a*e^(ax)

so:
if f(x)=(1/3)e^(3x) + (1/2)e^(-3x)
then f'(x)=(1/3)*3e^(3x) + (1/2)*(-3)e^(-3x)
=e^(3x) + (-3/2)e^(-3x)

finally f'(0) = 1 - 3/2 = -1/2 (as e^0 = 1)

Answer 4

e is a number . e = 2.71....

f(0) = 1/3 e^0 + 1/2e^0=1/3 + 1/2 = 2/6 + 3/6 = 5/6

Answer 5

e=2.71828182... is a mathematical constant


derivative of e^(ax) is { a * e^(ax) }

e^0 =1

so f(x)= (1/3) e^(3x) + (1/2)e^(-3x)
differentiating w.r.t.x

f ' (x) = (3/3) e^(3x) + (-3/2)e^(-3x)

put x =0


f ' (0) = 1 - (3/2) = -1/2

Answer 6

"e" is Euler's number, named after Leonhard Euler. You can learn about it here:
http://en.wikipedia.org/wiki/E_%28mathematical_constant%29

e is an irrational number, but here's the first 100 digits:

2.
7182818284590452353602
8747135266249775724709
3699959574966967627724
0766303535475945713821
78525166427

Answer 7

re e:

The natural logarithm, formerly known as the hyperbolic logarithm, is the logarithm to the base e, where e is an irrational constant approximately equal to 2.718281828459.
http://en.wikipedia.org/wiki/Natural_logarithm

Answer 8

yeah the first answer...e = 2.71.....