Find the 5th Derivative of the following. pls. show the solutions?

Question

FORM:
f(x) = mx^n
f'(x) = mnx^n-1



1. square root of x^5.
2. square root of 2x.
3. 3/x^2
4. 5x^5/x
5.square root of 2/x
6. 5x+99
7. 3x^6+2
8. square root of 2x^3
9. square root of 3x^2
10. 4/5x

Answer 1

if
f(x) = mx^n
f'(x) = mnx^(n-1)
f''(x) = mn(n-1)x^(n-2)
f'''(x) = mn(n-1)(n-2)x^(n-3)
f''''(x) = mn(n-1)(n-2)(n-3)x^(n-4)
and f''''(x) = mn(n-1)(n-2)(n-3)(n-4)x^(n-5)

so all you need to do is identify m and n in each of the following:
1) sqrt(x^5) = x^(5/2) so m = 1 and n = 5/2
so the 5th derivative is 2.5*1.5*.5*-.5*-1.5*x^-2.5
2) sqrt(2x) = sqrt(2)*x^.5, so m = sqrt(2) and n = .5
3) 3/x^2 = 3x^-2, so m = 3 and n = -2
get the idea?

Answer 2

First clarify your formula:
f(x) = mx^n
f'(x) = mnx^(n-1)

Now:
1. square roor of x^5= (x^5)^(1/2) = x^(5/2)
Derivative = (5/2)x^(5/2-1) = (5/2)x^(3/2)

2. etc.