Reference no: EM13127743

In each of the following parts, you should simplify your answers where it is appropriate to do so.

(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)

(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)

(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