Question

Which is the first and second derivative of the following function?

Answer 1

\[f(x)=\sqrt{3x+4}\]

Answer 2

\[f^{(1)}=? and f^{(2)}=?\]

Answer 3

@roobert95 hi..

Answer 4

Do you know chain rule?.

Answer 5

check the attachment

Answer 6

I'm sorry but i still cant solve the second derivative :(

Answer 7

@Princer_Jones can you please help me with the second one too?

Answer 8

Can you do the first derivative?

Answer 9

@Princer_Jones did the first derivative in the attachment

Answer 10

But can you do it?

Answer 11

no, not really

Answer 12

Suppose it was: \[
\sqrt{u}
\]Can you find the derivative of it?

Answer 13

yes, it's 1/2u^-1/2

Answer 14

The chain rules says that \[
\frac {df}{dx} = \frac{df}{du}\frac{du}{dx}
\]

Answer 15

I let \(u = 3x+4\)

Answer 16

Then \[
f(x)= \sqrt{u}
\]

Answer 17

You just found \[

\frac{df}{du} = \frac 1{2\sqrt u}
\]

Answer 18

Can you find the derivative of \(3x+4\)?

Answer 19

Because that will give us \(du/dx\).

Answer 20

the derivative of 3x+4 is 3

Answer 21

i'm sorry, what does du stand for?

Answer 22

So \[
\frac{df}{dx}=\frac{1}{2\sqrt{u}}\times 3
\]But we substitute back in the \(u=3x+4\): \[
\frac{df}{dx}=\frac{3}{2\sqrt{3+4}}
\]

Answer 23

The \(du\) is the infinitesimal change in \(u\).

Answer 24

It's basically \(\Delta u\) as it goes toward \(0\).