Question

Let f(x) = sqrt{7x^{2}+5}. Find f'(x).

Answer 1

You should use the chain rule,
\[f(x)=\sqrt{g(x)+k}\Rightarrow f'(x)=\frac{g'(x)}{2\sqrt{g(x)+k}}\]

Answer 2

Do you understand it?

Answer 3

Is g'(x)= 14x?

Answer 4

Perfect.

Answer 5

so would i leave it like \[14x \div2\sqrt{7x ^{2}+5}\]?

Answer 6

Yes, that is the right answer.

Answer 7

You can now simplify a little,
\[f'(x)=\frac{2x}{\sqrt{7x^2+5}}\]

Answer 8

its telling me that its not the answer

Answer 9

Sorry, I simplified the wrong way. It must be,
\[f'(x)=\frac{7x}{\sqrt{7x^2+5}}\]
As you see in the last formula you wrote (only divide by 2).

Answer 10

okay i was wondering how you got that 2. okay i see how you did that thank you very much!!!

Answer 11

;)