What is the derivative of $g (x) = x + (\frac{4}{x})$ $g(x)=x+(4/x)$ ?

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Answer 1 · 2018-07-30T20:24:21

$g'(x) = 1-4/(x^2)$

To find the derivative of $g(x)$ , you must differentiate each term in the sum

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

It is easier to see the Power Rule on the second term by rewriting it as

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

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

$g'(x) = 1 + 4(-1x^(-1-1))$

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

$g'(x) = 1 - 4x^-2$

Finally, you can rewrite this new second term as a fraction:

$g'(x) = 1-4/(x^2)$

Answer 2 · 2018-07-30T20:30:35

$g'(x)=1-4/(x^2)$

What might be daunting is the $4/x$ . Luckily, we can rewrite this as $4x^-1$ . Now, we have the following:

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

We can use the Power Rule here. The exponent comes out front, and the power gets decremented by one. We now have

$g'(x)=1-4x^-2$ , which can be rewritten as

$g'(x)=1-4/(x^2)$

Hope this helps!

What is the derivative of g(x)=x+(4/x)g(x)=x+(4x)g(x)=x+(4/x)?