How do you find the derivative of $x+4/x$ ?

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Answer 1 · 2015-10-19T16:43:43

See the explanation.

$d/dx(x+4/x) = d/dx(x)+d/dx(4/x)$

$= d/dx(x)+4d/dx(1/x)$

$= d/dx(x)+4d/dx(x^(-1))$

$= 1 + 4(-1x^-2)$

$= 1-4/x^2$

Or, more briefly:

$d/dx(x+4/x) = d/dx(x+4x^(-1))$

$= 1-4x^-2$

$= 1-4/x^2$

How do you find the derivative of x+4/xx+4/x?