Assignment:
Q1. 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)
Q2. 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)
Q3. 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
Q4. 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]
Provide complete and step by step solution for the question and show calculations and use formulas.