Class 12 Maths Exercise 3.5 New KPK Book | Class 12 Maths Ex 3.5 KPK Book | FBISE Differentiation | Study With Me
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1. Use the first principle rule to differentiate the following functions:-
a. f(x) = e2x
b. f(x) = (1/3) e3x
c. f(x) = (5/8) ex2+1
d. f(x) = 2x
e. f(x) = 4x+4
f. f(x) = log(x+1)
g. f(x) = logax2
h. f(x) = sinh2x
2. Find f’(x) if f(x) is:
a. y = 11(3-4x5)
b. y = esqrt(x)-5
c. y = x5.e1/x
d. y = e2x/ e-2x+1
e. y = ln(emx - e-mx)
f. y = eax-e-ax/ eax+e-ax
3 . Use any rule of differentiation to perform dy/dx for
a. y = x3.lnx
b. y = x2.(lnx)
c. y = ln(x2+1)/(x2-1)
d. y = ln(x-(x2+1)
e. y = e 2x.cos(2x)
f. y = x2.esin(x)
4 . Differentiate the following functions
a. y = log(x+2)3
b. y = cosh(3x)
c. y = sinh-1(cosx)
d. y = tanh 1(x/2)
e. y = ln(coth(x))
f. y = x.cosh-1(x)-sqrt(x2-1)
5. A research group (used hospital records) and developed the approx mathematical model related to systolic blood pressure and age : P(x) = 40+ 25ln(x+1) ,0 ≤ x ≤ 65 , where P(x) is the pressure measured in mm’s of mercury and x is age in years. What is the rate of change of pressure at the end of 10 years? at the end of 30 years? and at the end of 60 years ?
6. A single cholera bacterium divides every 0.5 hour to produce two complete cholera bacteria. If we start with a colony of 5000 bacteria then after ‘t’ hours there will be a A(t) = 5000 22t bacteria. Find A’(t), A’(1) and A’(5). Interpret the results.
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