# Derivatives, Product Rule, Quotient Rule, and Composite Rule

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, diï¬€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, diï¬€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, diï¬€erentiate the function

f(x) = (cos(1/2x))^4

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#### Solution Summary

The solution gives detailed steps on finding the derivatives for various questions using product rule, quotient rule and composite rule. All formula and calculations are shown and explained.