SUPER AWESOME MATH PROBLEM

Question

Derivative of e^-(1/1+x)?

Answer 1

Apply derivative with respective  x to each side for above function

The derivative of 1 / (1+ x) = -1 / (1 + x)² and derivative of e^x = e^x.

d / dx (e^{-1/(1 + x)})         = e^{-1/(1 + x)} × 1 / (1+ x)² ×(o + 1)

                                 = e^{-1/(1 + x)} × 1 / (1+ x)²

                                 =[e^{-1/(1 + x)} ] / (1+ x)² .

 

 

 

Answer 2

 

Possible derivation:

d/dx(e^{(-(x+1 1/1))})

Rewrite the expression: e^{-(x+1 1/1)}= e^(-x-1)

d/dx(e^(-x-1))

Using the chain rule, d/dx(e^(-x-1)))= e^u( du)/( dx), where u = -x-1 and  d/du(e^u) = e^u:

e^(-x-1) (d/dx(-x-1))

Differentiate the sum term by term and factor out constants:

e^(-x-1) (d/dx(-1)-d/dx(x))

The derivative of -1 is zero:

e^(-x-1) (0-d/dx(x))

Simplify the expression:

e^(-x-1) (d/dx(x)))

The derivative of x is 1:

Answer: e^(-x-1)

Answer 3

i hope it helps a lil