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Derivatives and Integrals of Exp and Log Functions

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1. Find the derivatives for the following functions ("^" means "to the power of", sorry I can't do double exponents on my keyboard) :

a. f(X) = 100e10X

b. f(X) = e(10X-5)

c. f(X) = e^X3

d. f(X) = 2X2e^(1- X2)

e. f(X) = 5Xe(12- 2X)

f. f(X) = 100e^(X3 + X4)

g. f(X) = e^(200X - X2 + X100)

2. Find the derivatives for the following functions:

a. f(X) = ln250X

b. f(X) = ln(20X-20)

c. f(X) = ln(1- X2)

d. f(X) = ln(5X + X-1)

e. f(X) = Xln(12- 2X)

f. f(X) = 2Xln(X3 + X4)

g. f(X) = ln(200X - X2 + X100)

3. Find the indefinite intgrals for the following functions

a. f(X) = e6X

b. f(X) = e(5X-5)

c. f(X) = 5eX

d. f(X) = 1/(1+X)

e. f(X) = 5/X

4. Find the definite intgrals for the following functions

a. f(X) = e2X over the interval [2, 4]

b. f(X) = 2eX over the interval [0, 2]

d. f(X) = 2/(2+X) over the interval [2, 5]

e. f(X) = 10/X over the interval [3, 10]

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Twenty-four problems involving Derivatives and Integrals of Exponential and Logarithmic Functions are solved. The response received a rating of "5" from the student who originally posted the question.

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Chris Busu, PhD (IP)
Education
  • BSc, University of Bucharest
  • MSc, Ovidius
  • MSc, Stony Brook
  • PhD (IP), Stony Brook
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