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

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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, diﬀerentiate 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, diﬀerentiate 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, diﬀerentiate 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.

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