Question

Find the derivative with respect to x of the given combination at the given value of x.

problem attached

Answer 1

I'm so confused on how to get this answer.

Answer 2

were you able to find derivative of \(\sqrt {g(x)}\) first >

Answer 3

Yeah, I got \[\sqrt{16}\]

Answer 4

then I used the d(√u)= u ' / 2 √u formula

Answer 5

so I thought u' = 1 and u = √16

Answer 6

i get √16 = 4 * 2 = 8

Answer 7

but not sure where the 7 comes from :S

Answer 8

no, i meant derivative of \(\sqrt {g(x)}\)
which will come in terms of x and not constant....

Answer 9

use chain rule...

Answer 10

you'll also have g'(x) in the numerator...

Answer 11

\[d(\sqrt{g(x)})=\frac{1}{2\sqrt{g(x)}}g'(x)\]

Answer 12

yup...now x=3 will give u 7/8
right ?

Answer 13

because g'(3)=7

Answer 14

Yes. I didn't know I had to multiply by g'(x) .

Answer 15

now you know :)
any doubts ?

Answer 16

Nope. Thanks for the help :)

Answer 17

welcome ^_^