answersLogoWhite

0

By using the chain rule. Since the derivative of exp(x) is exp(x), the derivative of exp(exp(exp(x))) is exp(exp(exp(x))) times the derivative of what is inside the parentheses, i.e., exp(exp(exp(x))) times derivate of exp(exp(x)). Continue using the chain rule once more, for this expression.

User Avatar

Wiki User

11y ago

Still curious? Ask our experts.

Chat with our AI personalities

LaoLao
The path is yours to walk; I am only here to hold up a mirror.
Chat with Lao
JudyJudy
Simplicity is my specialty.
Chat with Judy
TaigaTaiga
Every great hero faces trials, and you—yes, YOU—are no exception!
Chat with Taiga

Add your answer:

Earn +20 pts
Q: How do you differentiate exp exp exp x?
Write your answer...
Submit
Still have questions?
magnify glass
imp
Continue Learning about Math & Arithmetic

How do you differentiate exp exp x?

Use the "chain rule" of differentiation: y=exp(exp(x)) taking ln both side in y=e x (1/y)dy/dx=e x dy/dx=y*e x dy/dx=exp(x+exp(x))


What is the derivative of a half to the power of x?

(1/2)x = 2-x = exp (ln 2-x) = exp( -x ln 2). Since d/dx exp(x) = exp(x), we can use the chain rule to find that: d/dx (1/2)x = -(ln 2) exp(-x ln 2).


What is the derivative of half to the power of x?

(1/2)x = 2-x = exp (ln 2-x) = exp( -x ln 2). Since d/dx exp(x) = exp(x), we can use the chain rule to find that: d/dx (1/2)x = -(ln 2) exp(-x ln 2).


What is the derivative of -exp to the -x?

x e^x +C


Why are negative square roots are on the real number line if square root of a negative number not a real number?

Negative square roots are just the opposite of positive square roots. Since square roots (of positive numbers) are real, the negative square roots are also real.Square roots of negative numbers are not real.Note that -1 = exp(Pi*i), so (-1)^(1/2) = exp((1/2)*Pi*i) = i.Note that exp(i*x) = cos(x) + i*sin(x), for instance by taking derivatives:(d/dx)(exp(i*x)) = i*exp(i*x), and(d/dx)^2(exp(i*x)) =(-1)*exp(i*x).This means that the second derivative of exp(i*x) equals -exp(i*x).The same property holds for cos(x) + i*sin(x):(d/dx)(cos(x) + i*sin(x)) = -sin(x) + i*cos(x)(d/dx)^2(cos(x) + i*sin(x)) = -cos(x) - i*sin(x) = -(cos(x) + i*sin(x)))Hence cos(x) + i*sin(x)) = C + Dx + exp(i*x), for some C and D.Comparing the values on both sides for x = 0, we find:1 = C+1, so C = 0 and for the first derivative:i = D + i, so D = 0.So cos(x) + i*sin(x)) = exp(i*x) for all x.by comparing x=0 for both functions and their first derivative. Since they coincide,