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

Not what you're looking for?

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

##### Purchase this Solution

##### 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.

##### Purchase this Solution

##### Free BrainMass Quizzes

##### Probability Quiz

Some questions on probability

##### Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

##### Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

##### Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.