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

1 Answer
Jul 22, 2016

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

Explanation:

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)))