Find the derivative and simplify. f(x)=(x)^1/2-1/(x)^1/2+1
2007-06-25 06:20:43 · 4 answers · asked by annhall90 1 in Science & Mathematics ➔ Mathematics
f(x)=(x)^1/2-1/(x)^1/2+1
f(x)=(x)^1/2-(x)^-1/2+1
f '(x)=1/2 *x ^-1/2 + 1/2* x^-3/2 + 0
f '(x)= 1/(2x^1/2) + 1/(2 x^3/2)
f ' (x)=1/(2√x) + 1/(2 √ x³)
2007-06-25 06:26:49 · answer #1 · answered by harry m 6 · 0⤊ 0⤋
(1/2)X^(1/2-1)-1(-1/2)(x^(-3/2))
=1/2x^(1/2)+1/2x^(3/2)+0
=1/2x^(1/2)+1/2(xsqrt(x))
I presume your +1 at the end is not below the denominator since it's not within brackets.
2007-06-25 06:31:48 · answer #2 · answered by cidyah 7 · 0⤊ 0⤋
f(x)=x^1/2 - 1/x^1/2 + 1 or f(x)= x^1/2 - x^-1/2 + 1
f'(x)=1/2x^-1/2 + 1/2x^-3/2
f'(x)=1/2x^-1/2 times (1+x^-1)
2007-06-25 06:48:05 · answer #3 · answered by arthur g 2 · 0⤊ 0⤋
f(x)=(x)^1/2-1/(x)^1/2+1
This could be interpreted in different ways because you have not used parentheses properly to eliminate confusion.
It could be (x^.5 -1)/(x^.5 +1), or it could be:
x^.5 - 1/x^.5 + 1, or even
x^.5 - 1/(x^.5 + 1).
The reader should not be made to guess.
2007-06-25 06:56:14 · answer #4 · answered by ironduke8159 7 · 0⤊ 0⤋