Step-by-Step Differentiation Help for 2x(x+4)^8 and x/(x+2)^2

In summary, differentiation is a mathematical process used to find the rate of change between two quantities. To differentiate a polynomial function, the power rule can be used. The chain rule is used for differentiating composite functions. To differentiate a function with a fractional exponent, the power rule for fractional exponents can be used. A step-by-step guide for differentiating 2x(x+4)^8 and x/(x+2)^2 involves using the power rule, chain rule, and quotient rule.
  • #1
haywattsngu
3
0
Differentiation help <URGENT>

I have two functions to differentiate.

1) 2x(x+4)^8

2) x/(x+2)^2

If possible, please include step-by-step instructions.
 
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  • #2
1. [tex] f(x) = {2x(x+4)^{8}} [/tex]

Have you tried using the product rule?

2. [tex] f(x) = \frac{x}{(x+2)^{2}} [/tex]

Have you tried using the quotient rule?
 
  • #3
Make sure that you understand the chain rule for #1, if you don't know how to apply it in your sleep yet, keep practicing.
 
  • #4
I actually got the first answer after I posted! Anyway, thanks for all your help.
 
  • #5
I actually got the first answer after I posted!
 

FAQ: Step-by-Step Differentiation Help for 2x(x+4)^8 and x/(x+2)^2

1. What is differentiation?

Differentiation is a mathematical process used to find the rate at which one quantity changes with respect to another. It is commonly used in calculus to find the slope of a curve at a specific point.

2. How do I differentiate a polynomial function?

To differentiate a polynomial function, you can use the power rule, which states that the derivative of xn is nxn-1. For example, the derivative of 2x3 is 6x2.

3. What is the chain rule in differentiation?

The chain rule is a rule used to differentiate composite functions, which are functions that are made up of two or more functions. It states that the derivative of f(g(x)) is equal to the derivative of f evaluated at g(x) multiplied by the derivative of g(x).

4. How do I differentiate a function with a fractional exponent?

To differentiate a function with a fractional exponent, you can use the power rule for fractional exponents, which states that the derivative of xa/b is equal to (a/b)xa/b-1. For example, the derivative of x3/2 is (3/2)x1/2.

5. Can you provide a step-by-step guide for differentiating 2x(x+4)^8 and x/(x+2)^2?

Step 1: Use the power rule to differentiate 2x1 = 2.

Step 2: Use the chain rule to differentiate (x+4)^8 = 8(x+4)7.

Step 3: Simplify the expression to 2(8)(x+4)7 = 16(x+4)7.

Step 4: Use the quotient rule to differentiate x/(x+2) = (x+2)(1) - x(1) / (x+2)2 = (x+2-x) / (x+2)2 = 2 / (x+2).

Step 5: Use the chain rule to differentiate (x+2)^2 = 2(x+2)(1) = 2(x+2).

Step 6: Simplify the expression to 2 / 2(x+2) = 1 / (x+2).

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