How do you find the third derivative of $y = x^{2} - \frac{2}{x}$ $y=x^2-2/x$ ?

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Answer 1 · 2018-04-05T20:39:44

$=>f'''(x)=12/x^(4)$

We have:

$f(x)=x^2-2/x$ We can rewrite this as:

$f(x)=x^2-2x^-1$ We use the power rule:

$d/dx[x^n]=nx^(n-1)$ if $n$ is a constant.

$f'(x)=d/dx[x^2]-d/dx[2x^-1]$

$=>f'(x)=d/dx[x^2]-2*d/dx[x^-1]$

$=>f'(x)=2*x^(2-1)-2*-1*x^(-1-1)$

$=>f'(x)=2x-2*-x^(-2)$

$=>f'(x)=2x+2x^(-2)$ Repeat the process.

$=>f''(x)=d/dx[2x]+d/dx[2x^(-2)]$

$=>f''(x)=2*1*x^(1-1)+2*-2*x^-3$

$=>f''(x)=2-4x^-3$ Again!

$=>f'''(x)=d/dx[2]-d/dx[4x^-3]$

$=>f'''(x)=0-4*-3*x^(-3-1)$

$=>f'''(x)=0+12*x^(-4)$

$=>f'''(x)=12*1/x^(4)$

$=>f'''(x)=12/x^(4)$

How do you find the third derivative of y=x^2-2/xy=x2−2xy=x^2-2/x?