Calculus: The Language of Change

Exercise Set 6.5
General Exponentials

by Sharon Portz

Exercise 1 : Derivatives (dy/dt)

For y[t] as follows, find (dy/dt)[t]:

a) y = (3^t)			b) y = (10^t)				c) y = (a^t)

d) y = (t^t)			e) y = (2^Cos)[t]				f) y = t (e^t)

g) y = (e^((1/t)))			h) y = (3^((Sqrt[t])))				i) y = (Sqrt[(3^t) -  (2^t)])

Check your work with the computer.

part a

a) y = (3^t)

Solution of part a

Using WalkD we get:

part b

b) y = (10^t)

Solution of part b

part c

c) y = (a^t)

Solution of part c

part d

d) y = (t^t)

Solution of part d

part e

e) y = (2^Cos)[t]

Solution of part e

part f

f) y = t (e^t)

Solution of part f

\(\(
WalkD[E\^t\ t, t]\)\)

part g

g) y = (e^((1/t)))

Solution of part g

\(\(
WalkD[E\^\(1\/t\), t]\)\)

part h

h) y = (3^((Sqrt[t])))

Solution of part h

part i

i) y = (Sqrt[(3^t) -  (2^t)])

Solution of part i

Exercise 2 : Derivatives (dy/dx)

Find (dy/dx)[x]

a) y = (x^x)			b) y = (x^Sin)[x] 			c) y = (((Cos[x]))^x)

part a

a) y = (x^x)

Solution of parta

part b

b) y = (x^Sin)[x]

Solution of part b

part c

c) y = (((Cos[x]))^x)

Solution of partc