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# Derivative of function?

F(x)= square root(x) + 7 / square root (x) - 7

Find Fprime(x)

### 3 Answers

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- Anonymous1 decade agoFavorite Answer
F'(x)=(1/2 )x^{-1/2} -(7/2) x^{-3/2}

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- GuruLv 61 decade ago
here it is

F'(x) = (1/2)x^(-1/2) - (7/2)*x^(-3/2)

Take each term separately.

square root of x can be written as x^(1/2)

So, its derivative is (1/2) x^(1/2-1) = (1/2)x^(-1/2)

Do this for the second term also.

The third term, '7' is just a constant, so its derivative is just zero.

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- Mein Hoon NaLv 71 decade ago
you can find the value by u/v formula I think you mean

(sqrt(x) +7)/(sqrt(x)-7)) else it too trivial

d(u/v)/dx = (udv/dx - vdu/dx)/v^2

u = x^(1/2)+7

du/dx = (1/2) x^(-1/2)

and v = x^(1/2) - 7

dv/dx = (1/2) x^(-1/2)

so numerator = (x^(1/2)+7) (1/2)x^(-1/2) + (x^(-1/2)-7) (1/2)x^(-1/2)

= x^(1/2)x^(-1/2) = 1

denominator = (x^(1/2) - 7)

so f'(x) = 1/(x^(1/2)-7)^2

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