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

problem attached

Question

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

anonymous · Answer

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

hartnn · Answer

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

anonymous · Answer

Yeah, I got $$\sqrt{16}$$

anonymous · Answer

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

anonymous · Answer

so I thought u' = 1 and u = √16

anonymous · Answer

i get √16 = 4 * 2 = 8

anonymous · Answer

but not sure where the 7 comes from :S

hartnn · Answer

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

hartnn · Answer

use chain rule...

hartnn · Answer

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

stamp · Answer

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

hartnn · Answer

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

hartnn · Answer

because g'(3)=7

anonymous · Answer

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

hartnn · Answer

now you know :)
any doubts ?

anonymous · Answer

Nope. Thanks for the help :)

hartnn · Answer

welcome ^_^