The Derivative of ex:
Lab 7 TI-89 Calculus 1 The Derivative Formulas 03/01/06
Differentiate the functions in #1 - 20, and practice your algebra in simplifying their derivatives. Compare your answers and techniques within your lab group.
1.) [pic] 11.) [pic]
2.) [pic] 12.) [pic]
3.) [pic] 13.) [pic]
4.) f(x) = xk -kx 14.) p(q) = etan(sin q)
5.) [pic] 15.) [pic]
6.) G(r) =(ar2 + b)e-ct 16.) [pic]
7.) [pic] 17.) [pic]
8.) [pic] 18.) [pic]
9.) [pic] 19.) [pic]
10.) [pic] 20.) t(s) = cos((3s - ()2)
Consider the values of the following derivatives:
[pic][pic][pic] [pic] [pic] [pic]
Find the value of each of the following derivatives when t = 3:
21.) [pic] 22.) [pic] 23.) [pic] 24.) [pic]
25.) Find the equation of the line tangent to the curve [pic] when x = - 1.
26.) The position of a moving particle is given by s(t) = t sin(2t) where s measures distance in meters from the initial position and t is measured in seconds. Find the velocity and acceleration of the particle 5 seconds after the initial time.
27.) A stone is thrown into a still lake and causes a circular ripple. If the radius of the ripple is increasing at 2 feet per second, how fast is the area changing when the radius is 10 feet?
28.) The radius of a spherical balloon is increasing at 2 cm/sec. At what rate is air being blown into the balloon at the moment when the radius is 10 cm?
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