Question

Find f'x=√sin(8x)

Answer 1

\(f'(x) =(\sqrt )'* (sin)' *(8x)'\) . It is called chain rule.

Answer 2

Oh okay so when I derive it I get 4cos(8x)/sin(8x)

Answer 3

\((\sqrt)' = \dfrac{1}{2(\sqrt) }\)

Answer 4

whatever we don't do, just copy, we don't touch the inside of square root yet, hence copy it.
\((\sqrt{everything})' = \dfrac{1}{2(\sqrt{everything}) }=\dfrac{1}{2\sqrt{sin(8x)}}\)

Answer 5

Okay and then I leave it like than on the bottom and on top I derive sin?

Answer 6

\((sin)' = cos \), again, what we didn't touch, let it there
\((sin (8x))'= cos (8x)

Answer 7

now (8x)' =8

Answer 8

combine them all
\(f'(x)= \dfrac{1}{2\sqrt{sin(8x)}}*cos (8x)*8\)

Answer 9

simplify more (8/2) =4 you jot down the final answer

Answer 10

4cos8x/sin8x