calculus 2 derivatives

Question

 

y= 3tan^-1(x-√(1+x^2))

 

finding derivative 

Answer 1

Let y = tan^-1(u) where u is a function of x And tan^-1 is arctan.

the derivative dy/dx = 1/(u² + 1) * u' where u'  is derivative of u wrt x.

with this you should be able to solve.

hope helpful

best - David 

Answer 2

Rewrite the function using rational exponents.

 

y = 3tan^-1[x - (1 + x²)^1/2]

 

 

Use the chain-rule, product rule and trigonometric differentiation to take the derivative.  To make it easier, rewrite this once more using substitution.

 

Let      w = x - (1 + x²)^1/2

 

 

Then you have

 

y = 3tan^-1(w)

 

 

So the derivative is

 

y' = 3w' / (1 + w²)