8 square root x

Question

solve derivatives

Answer 1

The first derivative of 8√x (which can be written 8x^½) is (½)8x^-½=4/√x.

The second derivative is (-½)4x^-3/2=-2/√x³.

The third derivative is (-3/2)(-2)x^-5/2=3/√x⁵.

The fourth derivative is (-5/2)3x^-7/2=-(15/2)/√x⁷.

The fifth derivative is (105/4)/√x⁹.

The nth derivative is (-1)ⁿ⁺¹((1)(3)(5)...(2n-3)/2^n-3)/√x^2n-1, where integer n>1.

For example, n=3 gives us (1)(3)/√x⁵=3/√x⁵; n=2 gives us -(1/½)/√x³=-2/√x³.