Question

Can someone help with this derivative question?

Answer 1

what is the derivative of [ f(x) ]^2 ?

Answer 2

2x, no?

Answer 3

There really isn't a function given, so I'm just getting the derivative of x^2 there,

Answer 4

@phi

Answer 5

the rule is
\[ \frac{d}{dx} u^2 = 2 u \ \frac{du}{dx}\]

Answer 6

in this case, u is f(x)

Answer 7

what do you get ?

Answer 8

16

Answer 9

before you put in any numbers, what is the expression you get ?

Answer 10

Is that correct? I just plugged in the derivative of f(x) from the graph an then multiplied it by 2.

Answer 11

first, use this rule with f(x) instead of u
\[ \frac{d}{dx} u^2 = 2 u \ \frac{du}{dx} \]

what expression do you get ?

Answer 12

2f(x)

Answer 13

you left off the df(x)/dx (also written f'(x) )

Answer 14

2f(x) f'(x) ohh! Duh duh duh

Answer 15

Wait I meant

Answer 16

if you had
\[ \frac{d}{dx} x^2 = 2 x \frac{dx}{dx} = x^2 \]
but for f(x) you get
\[ \frac{d}{dx} f(x)^2 = 2 f(x)\frac{df(x)}{dx} = 2 f(x) f'(x) \]

Answer 17

* 2x on the first line not x^2

Answer 18

Thank you phi! 96