Question

DERIVATIVES
Can someone check my work?

Answer 1

\[f(x) = 2.38x - \frac{ x^2 }{ 28000 } - 3300\]

\[2.38x - x^2(28000)^{-1} - 3300\]

\[2.38x - 2x(-1)(28000)^{-2}\]

\[2.39 + \frac{ 2x }{ 22000^{2} }\]

This is what I get but the solution says the last step is ( - ) not ( + )

Answer 2

and it should've been 2.39 not 2.38 all the way through

Answer 3

oh mine

Answer 4

28000 is not a variable

Answer 5

and another typo, it's actually 22000 not 28000 all the way down

Answer 6

\[f(x)=ax+\frac{x^2}{c}-e \\ \text{ \let } a,c,e \text{ be constants } \\ f'(x)= \frac{d}{dx} (ax)+\frac{d}{dx}(\frac{x^2}{c})-\frac{d}{dx}(e) \\ f'(x) =a \frac{d}{dx}(x)+\frac{1}{c} \frac{d}{dx} (x^2)-0 \\ \text{ this step I used constant multiple rule for first two terms } \\ \text{ and I use constant rule for last term }\]

Answer 7

well it says that the solution is \[2.39-\frac{ x }{ 11000 }\]

Answer 8

yes but you treated the constant like a variable
you cannot do that

Answer 9

\[\frac{d}{dx}(cf)=c \cdot \frac{d}{dx} f \text{ is constant multiple rule }\]

Answer 10

have you heard of this rule?

Answer 11

Is this different from the multiplication rule for derivatives?

Answer 12

\[\frac{d}{dx} \frac{x^2}{28000}=\frac{d}{dx} (\frac{1}{28000} \cdot x^2)= \frac{1}{28000} \frac{d}{dx} (x^2)\]

Answer 13

And for some reason, I've never really understood the \[\frac{ d }{ dx }\].....it seems to confuse me

Answer 14

it just means find the derivative with respect to x

Answer 15

do you know power rule?

Answer 16

you need that to differentiate x^2

Answer 17

yeah, it would be 2x

Answer 18

great...
so
\[\frac{d}{dx} \frac{x^2}{28000}=\frac{d}{dx} (\frac{1}{28000} \cdot x^2)= \frac{1}{28000} \frac{d}{dx} (x^2)=\frac{1}{28000}(2x)=\frac{x}{14000}\]

Answer 19

ok, so for previous problems when I was solving for relative extremas, following the textbook, I just carry down the exponent for each individual # that had a variable

EX.


what rule is that?