Response the below:
1. Obtain dy/dx for the following expressions.
(a) y = (5x + 4)3
(b) y = (3 - 2x)5
(c) y = square root (5 - 0.6x)
(d) y = (2 + 3x)-0.6
2. Differentiate the following with respect to o.
(a) f(o) = sin(5o - 2)
(b) f(o) = cos(4 - 3o)
(c) f(o) = 7sin2(1 - 5o)
(d) f(o) = 2cos1/2(0.5o + 2.1)
3. The distance of a body from a point is given by s = xsin(wt + &). Show that the velocity and acceleration are given by v = xwcos(wt + &) and a = -w2s.
4. Differentiate f(x) = In(5x - 7) with respect to x.
5. Obtain the derivative of f(t) = In(5 - 2 t/3).
6. Differentiate f(x) = e(2x + 5) with respect to x.
7. Determine f ' (t) if f(t) = G(1 - e-kt).
8. Determine f ' (y) if f(y) = exp(3 - 1 y/4).
9. The charge of a capacitor is given by the function
q = qoe-kt
Where qo is the initial charge and k is a constant. Given that current is the rate of change of charge with respect to time, show that the value of the current when the charge has fallen to half the initial value is equal to -qok/2.