Home > Calculus > Power Rule

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

Answer 1

Charles Arocha

#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)#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Evelyn Agard

#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!

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 3

Charles Arocha

The derivative of ( g(x) = x + \frac{4}{x} ) is ( g'(x) = 1 - \frac{4}{x^2} ).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.