How to Derive 1/sqrt(1+2t)?

[ofiveo]

Practice problems for exam, sort of stuck
Question:

I can't seem to format it correctly so I'll write it by text

1/sqrt(1+2t)

The final answer is

1+t/sqrt(1+2t)^3Thank you

 

[Mark44]

Do we get to guess what the question is?

Also, I can't tell what you are trying to write in the second expression you show.

 

[HallsofIvy]

Since you titled this "differentiation", I will guess that you are asking about the derivative of
$$f(x)= \frac{1}{\sqrt{1+2t}}$$

Write it as $f(x)= (1+ 2t)^{-1/2}$ and use the "power rule" and the "chain rule":
$$f'(x)= -\frac{1}{2}(1+ 2t)^{-3/2}(2)= -\frac{1}{(\sqrt{1+ 2t})^3}$$
That is neither
$$1+ \frac{t}{(\sqrt{1+ 2t})^3}$$
nor
$$\frac{1+ t}{(\sqrt{1+ 2t})^3}$$