Question

find derivative: f(u) = arctan(u/(1+u)

Answer 1

1/(2u^(2)+2u+1)

Answer 2

oh is it because you need to foil them out?

Answer 3

arctan u/(1+u)

Remove the factor of 1 from the numerator.
1/(v^(2)+1)

Use the quotient rule to find the derivative of u/(1+u). The quotient rule states that ((f)/(g))'=(f'g-fg')/(g^2)'

d/dx [u]((1+u))-(u)((d)/(dx) [(1+u)]))/(((1+u))^(2))

Simplify the derivative.
d/dx u/(1+u)=1/(1+u)-u/(1+u)^(2)

Remove the factor of 1 from the numerator.
(1)/(1+u)-(u)/((1+u)^(2))

Simplify the derivative.
d/du arctan u/(1+u)=1/(2u^(2)+2u+1)

Remove the factor of 1 from the numerator.
1/(2u^(2)+2u+1)

Answer 4

ok i think i get it but then how about this one? f(x) = cos(arcsin(x+1))

Answer 5

\[\cos(\arcsin(x+1))\]
Add 0 to 1 to get 1
\[\frac{d}{dx}x+1=1\]
Simplify the derivative
\[\frac{d}{dx}\arcsin(x+1)=\frac{1}{\sqrt{-x(2+x)}}\]
Simplify the derivative
\[\frac{d}{dx}\cos(\arcsin(x+1))=-\frac{\sin((\arcsin(x+1))}{\sqrt{-x(2+x)}}\]
The derivative of cos(arcsin(x+1) is
\[-\frac{\sin((\arcsin(x+1))}{\sqrt{-x(2+x)}}\]

Answer 6

thanks! :)