Find the derivative of the function, f(x) = 5 Sin(120 pi t + pi/3) Find the deri

Question

Find the derivative of the function, f(x) = 5 Sin(120 pi t + pi/3) Find the derivative of the function, f(t) = 6e^5t Find the derivative of the function, f(x) = 7x^3 ln(6x) Find dy/dx for the following equation implicitly x^4 + 5x^3 y^2 = 5x^2 + 4(x+y) When a charged capacitor is discharged through a circuit of comparatively high resistance, the decay of the charge proceeds according to an exponential function of time, in accordance with the equation: q = Qe^-t/Rc If the total charge on the capacitor, Q, is a constant, and the "time constant", Rc, is a constant write the equation for current as a function of time. An electro-motive force, emf. is induced in a coil when there is any change in the magnetic field threading it. whether that change is caused by the motion of a bar magnet, a change in the current in a neighboring coil, or by a change in the current in the coil itself. This emf is directly proportional to the lime rate of change of current. If the proportionality constant is minus one times inductance, -L, write this as an equation If the current is described by the equation: i = 10Cos(120 pi t + pi/4), write the equation for emf. A robot arm moves in a circular path where the elbow, taken to be the center of the circle, located at the origin and the radius is the distance from the elbow to the gripper, 10 inches. For -5

Explanation / Answer

1)

f(t) = 5*sin (120*pi*t + pi/3)

f'(t) = 5*cos (120*pi*t + pi/3) * d/dt (120*pi*t + pi/3)

= 120*pi*5*cos (120*pi*t + pi/3)

=600*pi*cos (120*pi*t + pi/3)

2)

f(t) = 6e^(5t)

f'(t) = 6*d/dt (e^(5t))

= 6*5*e^(5t)

= 30*e^(5t)

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