Question

I have the answer can someone check me please..
Find the derivative of f(x)=(5/square rootx)

Answer 1

\[f(x)=\frac{ 5 }{ \sqrt{x} }\]

Answer 2

write is like this
\[ f(x) = 5 x^{-\frac{1}{2}} \]
and use the "power rule"

Answer 3

\[\frac{d}{dx} a x^n = a\ n\ x^{n-1} dx \]

Answer 4

I got \[-\frac{ 5 }{ 2x ^{\frac{ 3 }{ 2 }} }\]

Answer 5

\[ 5\cdot - \frac{1}{2} x^{- \frac{1}{2} - \frac{2}{2} } = -\frac{5}{2} x^{-\frac{3}{2}}\]
which looks like your answer.

Answer 6

ok so then that is the answer right?

Answer 7

yes. x^(-3/2) can be written as 1/ x^(3/2)

Answer 8

ok thanks

Answer 9

Real quick questiondoes the negative go on the inside or outside of parenthesis
-(5.....or (-5.......

Answer 10

what parens?

Answer 11

when typing the answer is it (-5/2x^(3/2))or -(5/2x(3/2))

Answer 12

I would type (5/2) in parens so it is clear we have 5/2
the - can go in lots of places:
(-5/2) or -(5/2) or (5/-2)

Answer 13

ok thanks

Answer 14

in your case where you have the x term in the denominator, I would write it
-5/(2 x^(3/2))
with the parens around everything in the denominator

Answer 15

ok thanks

Answer 16

you could write it as
\[ -\frac{5}{2 x^{\frac{3}{2}}} =\frac{-5}{2 x^{\frac{3}{2}}} =\frac{5}{-2 x^{\frac{3}{2}}}\]