We appreciate your visit to Find the derivative of the function f x x4 3x3 x 5 2 f x 25 4x3 9x2 1 3 2f x 25 x4 3x3. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
The derivative of the function f(x) = √(x⁴ - 3x³ + x)⁵ is given by f'(x) = (5/2) × √(x⁴ - 3x³ + x)³ × (4x³ - 9x² + 1).
To find the derivative of the function f(x) = √(x⁴ - 3x³ + x)⁵, we can use the chain rule and the power rule of differentiation. Let's proceed step by step:
Step 1: Rewrite the function using the exponentiation notation:
f(x) = √(x⁴ - 3x³ + x)⁵
Step 2: Apply the chain rule by differentiating the outer function with respect to the inner function:
f'(x) = (5/2) × (x⁴ - 3x³ + x[tex])^{\frac{5}{2} - 1 }[/tex]× d/dx (x⁴ - 3x³ + x)
Step 3: Differentiate the inner function, which involves applying the power rule:
f'(x) = (5/2) × √(x⁴ - 3x³ + x)³ × (4x³ - 9x² + 1)
Therefore, the derivative of the function f(x) = √(x⁴ - 3x³ + x)⁵ is given by f'(x) = (5/2) × √(x⁴ - 3x³ + x)³ × (4x³ - 9x² + 1).
To know more about derivative click here :
https://brainly.com/question/33847509
#SPJ4
The complete question is:
Find the derivative of the function f(x)= √(x⁴ − 3x³ + x)⁵
Thanks for taking the time to read Find the derivative of the function f x x4 3x3 x 5 2 f x 25 4x3 9x2 1 3 2f x 25 x4 3x3. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
