How do you find the derivative of #f(x)=(5x^6sqrt x) + (3/(x^3 sqrt x))#?

Answer 1

#f'(x) = 1/2(65x^5sqrt(x) -21/(x^4sqrt(x)))#

#f(x) = (5x^6sqrt(x)) + (3/(x^3sqrt(x)))#
Using the rules of indicies #f(x)# can be written:
#f(x) =5x^6x^(1/2) + 3x^-3x^(-1/2)# #= 5x^(13/2) + 3x^(-7/2)#

Aplying the Power Rule to both terms:

#f'(x) = 5* 13/2 x^(13/2-1) + 3* (-7/2) x^(-7/2-1)# #= 1/2(65x^(11/2) -21x^(-9/2))#
To express #f'(x)# in the form of #f(x)# in the original question, we can rewrite #f'(x)# as: #f'(x) = 1/2(65x^5 * x^(1/2) - 21x^(-4) * x^(-1/2))#
#=1/2(65x^5 sqrt(x) - 21/(x^4 sqrt(x)))#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To find the derivative of the function ( f(x) = 5x^6 \sqrt{x} + \frac{3}{x^3 \sqrt{x}} ), you can use the rules of differentiation:

  1. Apply the power rule to each term.
  2. Use the quotient rule for the second term.

After differentiating each term, the derivative of the function is:

[ f'(x) = 30x^5 \sqrt{x} + \frac{-9}{2x^4 \sqrt{x}} - \frac{3}{2x^5 \sqrt{x}} ]

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7