Question

derivative of sqrt(x) - 1/sqrt(x) ....would like to compare my steps with yours please

Answer 1

That looks like the antiderivative @surjithayer

Answer 2

\[d\left(\sqrt{x} - \frac{1}{\sqrt{x}}\right) \implies d(x^{1/2} - x^{-1/2})\]Use the rule \(d(x^n) = nx^{n-1}\)

Answer 3

oh sorry i thought anti derivative

Answer 4

Haha no it says find the DERIVATIVE. :)

Answer 5

yes, thank you, I did simplify to get the equation in the parentesis above

Answer 6

OK, now just take the derivative using the power rule for each term.

Answer 7

what would your next step be...I do use the power rule to find the derivative, but have the wrong answer when I simplify

Answer 8

always remember that : \(\large d(x^{1/2}) = \frac{1}{2\sqrt{x}}\)

Answer 9

yes

Answer 10

So same works with \(-x^{-1/2}\) but instead of having \(\frac{1}{2}\) in the denominator, you will have \(\frac{3}{2}\)

Answer 11

1/2sqrt(x^3)

Answer 12

That is correct.

Answer 13

can tha tsum be simplified?

Answer 14

\[\frac{1}{2x^{1/2}} +\frac{1}{2x^{3/2}}\] You can simplify it by multiplying the numerator and denominator of the first term by \(x\)

Answer 15

k

Answer 16

That way you will have \(2x^{3/2}\) as your common denominator.

Answer 17

quite helpful

Answer 18

Glad you got it, good luck.

Answer 19

your notation d for a derivative. (_)

Answer 20

\frac{d}{dx} is not much of a big deal to actually write out, but as long as the user understands it should be fine....

Answer 21

There are several notations for writing out the derivative :)

Answer 22

I haven't seen "d" beeing used like this, but it is just me....

Answer 23

and who cares after all, don't worry about it, you are right:)

Answer 24

Oh, it's used quite often, along with \(D_x\)

Answer 25

I knew only d/dx, or dy/dx , and the ' (the prime).