Question

Find the given higher-order derivative.

f''(x) = 9- 3/x

f'''(x)=

Answer 1

`f'''(x)=(3)/(x^(2))`

Explanation:

We are given with Second-order derivative of function f(x).

`f''(x)=9-(3)/(x)`

We need to find Third-order derivative of the function f(x).

`f''(x)=9-(3)/(x)=9-3x^(-1)`

We know that,

f'''(x) = (f''(x))'

So,

`f'''(x)=\frac{\mathrm{d}\,f''(x)}{\mathrm{d} x}`

`f'''(x)=\frac{\mathrm{d}\,(9-3x^(-1))}{\mathrm{d} x}`

`f'''(x)=\frac{\mathrm{d}\,9}{\mathrm{d} x}-\frac{\mathrm{d}\,3x^(-1)}{\mathrm{d} x}`

`f'''(x)=0-3\frac{\mathrm{d}\,x^(-1)}{\mathrm{d} x}`

`f'''(x)=-3(-1)x^(-1-1)`

`f'''(x)=3x^(-2)`

`f'''(x)=(3)/(x^(2))`

Therefore,
`f'''(x)=(3)/(x^(2))`