calculate derivative of f(x)=5x (x-1)^4
- print Print
- list Cite
Expert Answers
calendarEducator since 2010
write12,544 answers
starTop subjects are Math, Science, and Business
We have to find the derivative of f(x) = 5x * (x-1)^4
We can use the product rule here:
f(x) = 5x * (x-1)^4
f'(x) = (5x)' * (x-1)^4 + 5x * [(x-1)^4]'
=> f'(x) = 5* ( x - 1)^4 + 5x * 4*(x - 1)^3
=> f'(x) = 5(x - 1)^4 + 20x(x - 1)^3
The required derivative is f'(x) = 5*(x - 1)^4 + 20*x*(x - 1)^3
Related Questions
- Integrate f(x) = 1/(x^2 - 4)
- 1 Educator Answer
- Find the derivative of f(x) = 1+tan(x) / 1-tan(x)
- 2 Educator Answers
- What is the derivative of f(x)=4 cos ( 5x- 2). Please explain in detail.
- 1 Educator Answer
- `y = sqrt((x-1)/(x^4 + 1))` Use logarithmic differentiation to find the derivative of the...
- 1 Educator Answer
- Given the function f(x)=x^2-x^4, calculate (f o f o f o f)(1) .
- 1 Educator Answer
We also could expand the binomial and then we'll differentiate each term of the polynomial.
(x-1)^4 = x^4 - 4x^3 + 6x^2 - 4x + 1 (1)
Now, we'll multiply (1) by 5x:
5x(x-1)^4 = 5x(x^4 - 4x^3 + 6x^2 - 4x + 1)
5x(x-1)^4 = 5x^5 - 20x^4 + 30x^3 - 20x^2 + 5x
We'll differentiate with respect to x and we'll get:
f'(x) = 25x^4 - 80x^3 + 90x^2 - 40x + 5
We'll factorize by 5:
f'(x) = 5(5x^4 - 16x^3 + 18x^2 - 8x + 1)
Unlock This Answer Now
Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.
Student Answers