Question

(-1/2x).... how to find its third derivative?

Answer 1

Is that (1/2) times x
or (1/2) to the x power?
or 1 over (2x) ?

Answer 2

1 over 2x

Answer 3

(-1)/(2x)

Answer 4

.....its 2nd derivative is 1/x^3

Answer 5

@mathteacher1729

Answer 6

@Callisto

Answer 7

Re write your original expression
\[\huge f(x) = \frac{-1}{2x} =\frac{-1}{2}x^{-1}\]

Use the power rule
\[\huge f'(x)=(-1)\frac{-1}{2}x^{-2}=\frac{1}{2}x^{-2}\]

And again...
\[\huge f''(x)=(-2)\frac{1}{2}x^{-3}=-x^{-3}\]

And again... :)

Answer 8

@mathteacher1729 what is the power rule for that?

Answer 9

numerator times the derivative of denominator? @mathteacher1729

Answer 10

The power rule states that \[\huge \frac{d}{dx} (x^k) = k\cdot x^{(k-1)}\]

Answer 11

This holds even when k is negative. :)