How Do You Differentiate the Product of Two Functions Using the Chain Rule?

I don't think you can simplify further.In summary, the conversation discusses differentiating the expression (5x-1)^4)((8x^2-5)^-3) and the steps involved. The final result is (5x-1)^3)((8x^2-5)^-4)(-80x^2+48x -100).
  • #1
ahazen
49
0
I am trying to differentiate ((5x-1)^4)((8x^2-5)^-3) but i am stuck at a certain point...
Can you please help me fill in the blanks?

Thank you so much:):)


Work done:
1st step: (5x-1)^4 d/dx (8x^2-5)^-3 + (8x^2-5)^-3 d/dx(5x-1)^4

2nd step: (5x-1)^4 (-3)(8x^2-5)^-4 (16x)(8x^2-5)^-3 + (4)(5x-1)^3 (5)

3rd step: (I don't know what goes here...something x) (5x-1)^4 (8x^2-5)^-4 +9(5x-1)^4 (8x^2-5)^-3

Answer: 4(5x-4)^3 (8x^2-5)^-4 (I don't know what goes here)
 
Physics news on Phys.org
  • #2
f = ((5x-1)^4)((8x^2-5)^-3)
f' = ((5x-1)^4)'(8x^2-5)^-3) + ((5x-1)^4)((8x^2-5)^-3)'
f' = (4*5(5x-1)^3)(8x^2-5)^-3) + ((5x-1)^4)(16x*(-3)(8x^2-5)^-4)
simplify
f' = 20((5x-1)^3)((8x^2-5)^-3) -48x((5x-1)^4)((8x^2-5)^-4)
f' = ((5x-1)^3)((8x^2-5)^-4)(-80x^2+48x -100)

Not sure if this helps
 

Related to How Do You Differentiate the Product of Two Functions Using the Chain Rule?

1. What is the chain rule in calculus?

The chain rule in calculus is a formula used to find the derivative of a composite function. It states that the derivative of a composite function is equal to the derivative of the outer function multiplied by the derivative of the inner function.

2. Why is the chain rule important in calculus?

The chain rule is important in calculus because it allows us to find the rate of change of complex functions by breaking them down into simpler functions. It is a fundamental tool used in many areas of mathematics and science, such as physics, economics, and engineering.

3. How do you apply the chain rule in calculus?

To apply the chain rule in calculus, you first identify the inner and outer functions in the composite function. Then, you take the derivative of the outer function and multiply it by the derivative of the inner function. This gives you the derivative of the composite function.

4. Can you give an example of using the chain rule in calculus?

Sure, an example of using the chain rule in calculus is finding the derivative of the function f(x) = (x^2 + 1)^3. First, we identify the inner function as x^2 + 1 and the outer function as ( )^3. Then, we take the derivative of the outer function (3( )^2) and multiply it by the derivative of the inner function (2x). This gives us the derivative of the composite function f'(x) = 6x(x^2 + 1)^2.

5. Are there any shortcuts or tips for using the chain rule in calculus?

Yes, there are a few shortcuts and tips for using the chain rule in calculus. One is the "outside-inside" rule, where you first take the derivative of the outside function, then substitute the inside function for the variable and take its derivative. Another tip is to remember the chain rule as "derivative of the outside, times the derivative of the inside."

Similar threads

How Do You Simplify and Analyze Taylor Polynomials for Higher Degree Functions?
    • Calculus and Beyond Homework Help
Replies
5
Views
1K
Finding the Fourier Series of a step function
    • Calculus and Beyond Homework Help
Replies
5
Views
2K
I'm having some trouble differentiating radical functions
    • Calculus and Beyond Homework Help
Replies
6
Views
1K
Solve the given differential equation
    • Calculus and Beyond Homework Help
Replies
10
Views
1K
Solve the problem that involves iteration
    • Precalculus Mathematics Homework Help
Replies
21
Views
1K
Calculus Confusion over Calculus Book example footnote
    • Science and Math Textbooks
Replies
9
Views
1K
Find the two points on the curve that share a tangent line
    • Calculus and Beyond Homework Help
Replies
9
Views
1K
MHB Calculating the Derivative of a Function Using the Chain Rule
    • Calculus
Replies
2
Views
1K
Differentiating a a rational function
    • Calculus and Beyond Homework Help
Replies
3
Views
1K
Implicit differentiation: why apply the Chain Rule?
    • Calculus and Beyond Homework Help
Replies
3
Views
917

Hot Threads

Recent Insights

Back
Top