Discuss the below:
In each of the following parts, you should simplify your answers where it is appropriate to do so.
Q(1) (a) Write down the derivative of each of the functions
f(x) = e^-8x and g(x)=sin(4x)
(b) Hence, by using the Product Rule, di?erentiate the function
k(x) = e^-8xsin (4x)
Q(2) (a) Write down the derivative of each of the functions
f(t) = ln(6t) (t > 0) and g(t) = t^4 + 1
(b) Hence, by using the Quotient Rule, di?erentiate the function
k(t)=(ln(6t))/(t^4+1) (t>0)
Q(3) (a) Write down the derivative of the function
f(x) = cos1/2 x
(b) Hence, by using the Composite Rule, di?erentiate the function
f(x) = (cos(1/2x))^4