Question

y=sin sqrt(1+x^2) I know you use the chain rule to sort this out. im down to cos sqrt(1+x^2) (1/2 (2x)^-1/2 (2x) the book is telling me the derivative of sqrt 1+ x^2 is 1/2sqrt(1+x^2) which I dont understand entirely help would be appreciated.

Answer 1

well it isn't so i hope the book is not telling you that

Answer 2

the derivative of \(\sqrt{x}\) is \(\frac{1}{2\sqrt{x}}\) but the derivative of \(\sqrt{1+x^2}\) is \(\frac{x}{\sqrt{1+x^2}}\) by the chain rule

Answer 3

break that down for me if you can. the book breaks down the derivative like this, cos(\[\sqrt{1+x}^2\] 1/2\[\sqrt{1+x^2}\] (2x)

Answer 4

ok that was messed up.

Answer 5

it was cos(sqrt 1+x^2) 1/2sqrt(1+x^2) (2x)

Answer 6

1/2sqrt(1+x^2) this part I dont get. I know its the derivative of that sqrt function, I just dont understand how they did it.

Answer 7

I wrote it with fractional exponents, maybe that will be a little easier to read for you :)